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The development of more efficient catalytic processes and new approaches to control catalytic activity and selectivity are central to the realization of more selective, atom economic, and energy efficient routes to value added chemicals and polymers. The reactivity and selectivity of a transition metal catalyst is intimately related to the ligand-sphere geometry and, in many cases, the ideal ligand geometry for one step of a catalytic cycle is poorly matched to the ideal ligand geometry for another, resulting in sub-optimal efficiency. Macroscopic mechanical forces are both large, potentially much larger than interatomic forces, and are directional and localized to an extent that differentiates them from other forms of energy input such as heat or light. As such, mechanical force represents a heretofore untapped approach to modulate catalyst geometry, with the potential to reversibly modulate catalyst geometry on the timescale of catalytic turnover or monomer enchainment. This project has addressed the fundamental challenges in material-to-molecule strain coupling associated with the development of a new class of mechanically responsive catalysts (mechanocatalysts) in which active organotransition metal catalysts are strategically embedded in a flexible polymer network such that application of external mechanical force (stretching or deformation) leads to modulation of catalyst geometry, and hence reactivity and selectivity. Our efforts during the tenure of this grant were directed toward the elucidation of force-reactivity relationships of elementary transformations that occur within the first coordination sphere of a transition metal complex employing stiff stilbene photoswitches tethered to a flexible bidentate phosphine ligand derived from MeOBiphep as molecular force probes which provide a range of compressive and extension forces to the coupled transition metal complex depending on the geometry of the stiff stilbene and length of the tethering chains. During the tenure of this grant, we have quantified the rate of C(sp 2 )-C(sp 2 ) reductive elimination from platinum(II) diaryl complexes containing bis(phosphine) force probe ligands as a function of mechanical force; compressive forces decreased the rate of reductive elimination whereas extension forces increased the rate relative to the strain-free MeOBiphep complex with a 3.4-fold change in rate over a ~290 pN range of restoring forces. In a similar manner, we have quantified the rate of oxidative addition of bromobenzene to low-ligated palladium(0) complexes containing force probe ligands as a function of mechanical force; compressive forces increase the rate of oxidative addition, whereas tensile forces decrease the rate with a ~6 fold change in rate across ~340 pN of force applied to the complexes. In both cases, experimental and computational analyses argue strongly against any significant force-induced perturbation of ground state geometry within the first coordination sphere of the reactant complexes. Rather, the force/rate behavior observed for these transformations across these ranges of forces is attributed to the coupling of force to the nuclear motion comprising the reaction coordinates for reductive elimination and oxidative addition. These results together inform the development of catalysts whose activity can be tuned by an external force that is adjusted within a catalytic cycle and suggest opportunities to experimentally map geometry changes associated with reactions in transition metal complexes and potential strategies for force-modulated catalysis.
Here, the loss-of-equilibrium is a solar eruption mechanism whereby a sudden breakdown of the magnetohydrodynamic force balance in the Sun's corona ejects a massive burst of particles and energy into the heliosphere. Predicting a loss-of-equilibrium, which has more recently been formulated as the torus instability, relies on a detailed understanding of the various forces that hold the pre-eruption magnetic flux rope in equilibrium. Traditionally, idealized analytical force expressions are used to derive simplified eruption criteria that can be compared to solar observations and modeling. What is missing, however, is a validation that these idealized analytical force expressions can be applied to the line-tied, low-aspect-ratio conditions of the corona. In this paper, we address this shortcoming by using a laboratory experiment to study the forces that act on long-lived, arched, line-tied magnetic flux ropes. Three key force terms are evaluated over a wide range of experimental conditions: (1) the upward hoop force; (2) the downward strapping force; and (3) the downward toroidal field tension force. First, the laboratory force measurements show that, on average, the three aforementioned force terms cancel to produce a balanced line-tied equilibrium. This finding validates the laboratory force measurement techniques developed here, which were recently used to identify a dynamic toroidal field tension force that can prevent flux rope eruption. The verification of magnetic force balance also confirms the low-beta assumption that the plasma thermal pressure is negligible in these experiments. Next, the measured force terms are directly compared to corresponding analytical expressions. While the measured and analytical forces are found to be well correlated, the low-aspect-ratio, line-tied conditions in the experiment are found to both reduce the measured hoop force and increase the measured tension force with respect to analytical expectations. These two co-directed effects combine to generate laboratory flux rope equilibria at lower altitudes than are predicted analytically. Such considerations are expected to modify the loss-of-equilibrium eruption criteria for analogous flux ropes in the solar corona.
The loss-of-equilibrium is a solar eruption mechanism whereby a sudden breakdown of the magnetohydrodynamic force balance in the Sun's corona ejects a massive burst of particles and energy into the heliosphere. Predicting a loss-of-equilibrium, which has more recently been formulated as the torus instability, relies on a detailed understanding of the various forces that hold the pre-eruption magnetic flux rope in equilibrium. Traditionally, idealized analytical force expressions are used to derive simplified eruption criteria that can be compared to solar observations and modeling. What is missing, however, is a validation that these idealized analytical force expressions can be applied to the line-tied, low-aspect-ratio conditions of the corona. In this paper, we address this shortcoming by using a laboratory experiment to study the forces that act on long-lived, arched, line-tied magnetic flux ropes. Three key force terms are evaluated over a wide range of experimental conditions: (1) the upward hoop force; (2) the downward strapping force; and (3) the downward toroidal field tension force. First, the laboratory force measurements show that, on average, the three aforementioned force terms cancel to produce a balanced line-tied equilibrium. This finding validates the laboratory force measurement techniques developed here, which were recently used to identify a dynamic toroidal field tension force that can prevent flux rope eruptions [Myers et al., Nature 528, 526 (2015)]. The verification of magnetic force balance also confirms the low-beta assumption that the plasma thermal pressure is negligible in these experiments. Next, the measured force terms are directly compared to their corresponding analytical expressions. While the measured and analytical forces are found to be well correlated, the low-aspect-ratio, line-tied conditions in the experiment are found to both reduce the measured hoop force and increase the measured tension force with respect to analytical expectations. These two co-directed effects combine to generate laboratory flux rope equilibria at lower altitudes than are predicted analytically. Such considerations are expected to modify the loss-of-equilibrium eruption criteria for analogous flux ropes in the solar corona.
In many pathological conditions the endothelium becomes activated and dysfunctional, resulting in hyperpermeability and plasma leakage. No specific therapies are available yet to control endothelial barrier function, which is regulated by inter-endothelial junctions and the generation of acto-myosin-based contractile forces in the context of cell-cell and cell-matrix interactions. However, the spatiotemporal distribution and stimulus-induced reorganization of these integral forces remain largely unknown. Traction force microscopy of human endothelial monolayers was used to visualize contractile forces in resting cells and during thrombin-induced hyperpermeability. Simultaneously, information about endothelial monolayer integrity, adherens junctions and cytoskeletal proteins (F-actin) were captured. This revealed a heterogeneous distribution of traction forces, with nuclear areas showing lower and cell-cell junctions higher traction forces than the whole-monolayer average. Moreover, junctional forces were asymmetrically distributed among neighboring cells. Force vector orientation analysis showed a good correlation with the alignment of F-actin and revealed contractile forces in newly formed filopodia and lamellipodia-like protrusions within the monolayer. Finally, unstable areas, showing high force fluctuations within the monolayer were prone to form inter-endothelial gaps upon stimulation with thrombin. To conclude, contractile traction forces are heterogeneously distributed within endothelial monolayers and force instability, rather than force magnitude, predicts the stimulus-induced formation of intercellular gaps. - Highlights: • Endothelial monolayers exert dynamic- and heterogeneous traction forces. • High traction forces correlate with junctional areas and the F-actin cytoskeleton. • Newly formed inter-endothelial gaps are characterized by opposing traction forces. • Force stability is a key feature controlling endothelial permeability.
A magnetic field is force-free if there is no interaction between it and the plasma in the surrounding atmosphere, i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of various magnetic parameters, such as magnetic energy (using the virial theorem), gradient of twist of sunspot magnetic fields (computed from the force-free parameter {alpha}), and any kind of extrapolation, heavily hinges on the force-free approximation of the photospheric sunspot magnetic fields. Thus, it is of vital importance to inspect the force-free behavior of sunspot magnetic fields. The force-free nature of sunspot magnetic fields has been examined earlier by some researchers, ending with incoherent results. Accurate photospheric vector field measurements with high spatial resolution are required to inspect the force-free nature of sunspots. For this purpose, we use several vector magnetograms of high spatial resolution obtained from the Solar Optical Telescope/Spectro-Polarimeter on board Hinode. Both the necessary and sufficient conditions for force-free nature are examined by checking the global and local nature of equilibrium magnetic forces over sunspots. We find that sunspot magnetic fields are not very far from the force-free configuration, although they are not completely force-free on the photosphere. The umbral and inner penumbral fields are more force-free than the middle and outer penumbral fields. During their evolution, sunspot magnetic fields are found to maintain their proximity to force-free field behavior. Although a dependence of net Lorentz force components is seen on the evolutionary stages of the sunspots, we do not find a systematic relationship between the nature of sunspot magnetic fields and the associated flare activity. Further, we examine whether the fields at the photosphere follow linear or nonlinear force-free conditions. After examining this in various complex and simple sunspots, we conclude that, in either case, photospheric sunspot magnetic fields are closer to satisfying the nonlinear force-free field approximation.
It is a common practice in the solar physics community to test whether or not measured photospheric or chromospheric vector magnetograms are force-free, using the Maxwell stress as a measure. Some previous studies have suggested that magnetic fields of active regions in the solar chromosphere are close to being force-free whereas there is no consistency among previous studies on whether magnetic fields of active regions in the solar photosphere are force-free or not. Here we use three kinds of representative magnetic fields (analytical force-free solutions, modeled solar-like force-free fields, and observed non-force-free fields) to discuss how measurement issues such as limited field of view (FOV), instrument sensitivity, and measurement error could affect the estimation of force-freeness based on observed magnetograms. Unlike previous studies that focus on discussing the effect of limited FOV or instrument sensitivity, our calculation shows that just measurement error alone can significantly influence the results of estimates of force-freeness, due to the fact that measurement errors in horizontal magnetic fields are usually ten times larger than those in vertical fields. This property of measurement errors, interacting with the particular form of a formula for estimating force-freeness, would result in wrong judgments of the force-freeness: a truly force-free field may be mistakenly estimated as being non-force-free and a truly non-force-free field may be estimated as being force-free. Our analysis calls for caution when interpreting estimates of force-freeness based on measured magnetograms, and also suggests that the true photospheric magnetic field may be further away from being force-free than it currently appears to be.
Abstract. The effective radiative forcing, which includes the instantaneous forcing plus adjustments from the atmosphere and surface, has emerged as the key metric of evaluating human and natural influence on the climate. We evaluate effective radiative forcing and adjustments in 17 contemporary climate models that are participating in the Coupled Model Intercomparison Project (CMIP6) and have contributed to the Radiative Forcing Model Intercomparison Project (RFMIP). Present-day (2014) global-mean anthropogenic forcing relative to pre-industrial (1850) levels from climate models stands at 2.00 (±0.23) W m−2, comprised of 1.81 (±0.09) W m−2 from CO2, 1.08 (± 0.21) W m−2 from other well-mixed greenhouse gases, −1.01 (± 0.23) W m−2 from aerosols and −0.09 (±0.13) W m−2 from land use change. Quoted uncertainties are 1 standard deviation across model best estimates, and 90 % confidence in the reported forcings, due to internal variability, is typically within 0.1 W m−2. The majority of the remaining 0.21 W m−2 is likely to be from ozone. In most cases, the largest contributors to the spread in effective radiative forcing (ERF) is from the instantaneous radiative forcing (IRF) and from cloud responses, particularly aerosol–cloud interactions to aerosol forcing. As determined in previous studies, cancellation of tropospheric and surface adjustments means that the stratospherically adjusted radiative forcing is approximately equal to ERF for greenhouse gas forcing but not for aerosols, and consequentially, not for the anthropogenic total. The spread of aerosol forcing ranges from −0.63 to −1.37 W m−2, exhibiting a less negative mean and narrower range compared to 10 CMIP5 models. The spread in 4×CO2 forcing has also narrowed in CMIP6 compared to 13 CMIP5 models. Aerosol forcing is uncorrelated with climate sensitivity. Therefore, there is no evidence to suggest that the increasing spread in climate sensitivity in CMIP6 models, particularly related to high-sensitivity models, is a consequence of a stronger negative present-day aerosol forcing and little evidence that modelling groups are systematically tuning climate sensitivity or aerosol forcing to recreate observed historical warming.
Purpose: In mammography, the height of the image receptor is adjusted to the patient before compressing the breast. An inadequate height setting can result in an imbalance between the forces applied by the image receptor and the paddle, causing the clamped breast to be pushed up or down relative to the body during compression. This leads to unnecessary stretching of the skin and other tissues around the breast, which can make the imaging procedure more painful for the patient. The goal of this study was to implement a method to measure and minimize the force imbalance, and to assess its feasibility as an objective and reproducible method of setting the image receptor height. Methods: A trial was conducted consisting of 13 craniocaudal mammographic compressions on a silicone breast phantom, each with the image receptor positioned at a different height. The image receptor height was varied over a range of 12 cm. In each compression, the force exerted by the compression paddle was increased up to 140 N in steps of 10 N. In addition to the paddle force, the authors measured the force exerted by the image receptor and the reaction force exerted on the patient body by the ground. The trial was repeated 8 times, with the phantom remounted at a slightly different orientation and position between the trials. Results: For a given paddle force, the obtained results showed that there is always exactly one image receptor height that leads to a balance of the forces on the breast. For the breast phantom, deviating from this specific height increased the force imbalance by 9.4 ± 1.9 N/cm (6.7%) for 140 N paddle force, and by 7.1 ± 1.6 N/cm (17.8%) for 40 N paddle force. The results also show that in situations where the force exerted by the image receptor is not measured, the craniocaudal force imbalance can still be determined by positioning the patient on a weighing scale and observing the changes in displayed weight during the procedure. Conclusions: In mammographic breast compression, even small changes in the image receptor height can lead to a severe imbalance of the applied forces. This may make the procedure more painful than necessary and, in case the image receptor is set too low, may lead to image quality issues and increased radiation dose due to undercompression. In practice, these effects can be reduced by monitoring the force imbalance and actively adjusting the position of the image receptor throughout the compression.
We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.
Mechanical forces generated by myosin II molecular motors drive diverse cellular processes, most notably shape change, division and locomotion. These forces may be transmitted over long range through the cytoskeletal medium – a disordered, viscoelastic network of biopolymers. The resulting cell size scale force chains can in principle mediate mechanical interactions between distant actomyosin units, leading to self-organized structural order in the cell cytoskeleton. Inspired by such force transmission through elastic structures in the cytoskeleton, we consider a percolated fiber lattice network, where fibers are represented as linear elastic elements that can both bend and stretch, and the contractile activity of myosin motors is represented by force dipoles. Then, by using a variety of metrics, we show how two such contractile force dipoles interact with each other through their mutual mechanical deformations of the elastic fiber network. As a prelude to two-dipole interactions, we quantify how forces propagate through the network from a single anisotropic force dipole by analyzing clusters of nodes connected by highly strained bonds, as well as through the decay rate of strain energy with distance from a force dipole. We show that predominant fiber bending screens out force propagation, resulting in reduced and strongly network configuration-dependent dipole interactions. On the other hand, stretching-dominated networks support longer-ranged inter-dipole interactions that recapitulate the predictions of linear elasticity theory. By characterizing the differences between tensile and compressive force propagation in the fiber network, we show how inter-dipole interaction depends on the dipoles’ mutual separation and orientation. The resulting elastic interaction energy may mediate a force between multiple distant dipoles, leading to their self-organization into ordered configurations. In conclusion, this provides a potential pathway for active mechanical force-driven structural order in elastic biopolymer networks.
A scanning probe with an atomically sharp tip is used in atomic force microscopy. As the probe is rastered over the specimen of interest, changes in its vibration mode can be ascribed to changes in the interatomic forces between the specimen and the tip. Various modes for implementing atomic force measures exist. One of the most successful modes is frequency-modulation noncontact atomic force microscopy. Here we address the role of replicating accurate forces on the probe tip to simulate images within this mode. In this work, we examine several approaches. One involves the use of classical force fields based on interatomic potentials, where the potentials are often fit to experiment. Other approaches center on the use of forces generated from quantum-based calculations. We consider the development of a “virtual tip” approximation wherein the probe tip senses electrostatic forces generated by the specimen. This approach treats the specimen quantum mechanically, while the tip is treated as a classical object. We also consider the use of an embedding approximation to avoid direct computations of the specimen in the presence of the tip. In this method, the tip and specimen are treated quantum mechanically. However, the electronic structure of the specimen is computed in the absence of the probe tip. The electronic density of the specimen is then fixed and the electronic structure of the tip is then computed in the presence of the fixed density. As a general approach, we outline new methods for the full computation of quantum forces between the tip and specimen. We note that quantum-based forces are particularly important as they directly contain the chemical nature of the forces present without the use of any adjustable parameters. We illustrate recent algorithmic developments to computing quantum forces that can produce accurate simulations of atomic force microscopy images for large and complex molecular species. We also suggest new pathways to overcome current challenges in this rapidly evolving field.
The role of ocean forcing on Atlantic multidecadal variability (AMV) is assessed from the (downward) heat flux–SST relation in the framework of a new stochastic climate theory forced by red noise ocean forcing. Previous studies suggested that atmospheric forcing drives SST variability from monthly to interannual time scales, with a positive heat flux–SST correlation, while heat flux induced by ocean processes can drive SST variability at decadal and longer time scales, with a negative heat flux–SST correlation. Here, first, we develop a theory to show how the sign of heat flux–SST correlation is affected by atmospheric and oceanic forcing with time scale. In particular, a red noise ocean forcing is necessary for the sign reversal of heat flux–SST correlation. Furthermore, this sign reversal can be detected equivalently in three approaches: the low-pass correlation at lag zero, the unfiltered correlation at long (heat flux) lead, and the real part of the heat flux–SST coherence. Second, we develop a new scheme in combination with the theory to assess the magnitude and time scale of the red noise ocean forcing for AMV in the GFDL SPEAR model (Seamless System for Prediction and Earth System Research) and observations. In both the model and observations, the ocean forcing on AMV is in general comparable with the atmospheric forcing, with a 90% probability greater than the atmospheric forcing in observations. In contrast to the white noise atmospheric forcing, the ocean forcing has a persistence time comparable or longer than a year, much longer than the SST persistence of ~3 months. This slow ocean forcing is associated implicitly with slow subsurface ocean dynamics.
The tensor interaction is known to play an important role in the nuclear structure studies of exotic nuclei. However, most microscopic studies of low-energy nuclear reactions neglect the tensor force, resulting in a lack of knowledge concerning the effect of the tensor force on heavy-ion collisions. An accurate description of the heavy-ion interaction potential is crucial for understanding the microscopic mechanisms of heavy-ion fusion dynamics. Furthermore, the building blocks of the heavy-ion interaction potential in terms of the ingredients of the effective nucleon-nucleon interaction provides the physical underpinnings for connecting the theoretical results with experiment. The tensor force has never been incorporated for calculating the nucleus-nucleus interaction potential. The theoretical study of the influence of the tensor force on heavy-ion interaction potentials is required to further our understanding of the microscopic mechanisms entailed in fusion dynamics. The full Skyrme tensor force is implemented into the static Hartree-Fock and dynamic density-constrained time-dependent Hartree-Fock (DC-TDHF) theory to calculate both static (frozen density) and dynamic microscopic interaction potentials for reactions involving exotic and stable nuclei. The static potentials are found to be systematically higher than the dynamical results, which are attributed to the microscopic dynamical effects included in TDHF. We also show that the dynamical potential barriers vary more significantly by the inclusion of tensor force than the static barriers. The influence of isoscalar and isovector tensor terms is also investigated with the TIJ set of forces. For light systems, the tensor force is found to have an imperceptible effect on the nucleus-nucleus potential. However, for medium and heavy spin-unsaturated reactions, the potentials may change from a fraction of an MeV to almost 2 MeV by the inclusion of tensor force, indicating a strong impact of the tensor force on subbarrier fusion. The tensor force could indeed play a large role in the fusion of nuclei, with spin-unsaturated systems seeing a systematic increase in ion-ion barrier height and width. Furthermore, this fusion hindrance is partly due to static, ground-state effects from the inclusion of the tensor force, though additional hindrance appears when studying nuclear dynamics.
Via programs including the Light Water Reactor Sustainability and Integrated Energy Systems, the U.S. Department of Energy has invested in the Framework for Optimization of ResourCes and Economics (FORCE) software framework (Idaho National Laboratory 2024a) for the technical and economic analysis of nuclear-integrated energy systems (IES). Nuclear IES expand the use of nuclear from traditional baseload electricity generation to a flexible and adaptive source of combined heat and power. Nuclear heat can be used in the production of a variety of energy currencies such as hydrogen and ammonia as well as other heat applications including water desalination and district heating. FORCE is designed with the intent to provide interconnected analysis tools that enable the accurate technical and economic assessment of specific nuclear IES configurations for individual energy markets. FORCE consists of three main analysis pathways: HYBRID (Idaho National Laboratory 2024b), which contains high-resolution physical models for IES; Holistic Energy Resource Optimization Network (HERON) (Idaho National Laboratory 2024c), which analyzes IES long-term economic viability; and Optimization of Real-time Capacity Allocation (ORCA) (Idaho National Laboratory 2024d), designed for real-time control of IES via digital twins and optimal decision making, including autonomous and remote operation research. Development of the FORCE ecosystem is guided by three pillars: capability, which assures that the computational requirements of IES analysis are met by the software tools; reliability, which provides for consistent code performance and expected behaviors; and accessibility, which lowers the barrier to entry for using the software and accelerates analysis by users beyond the FORCE primary developers. Reliability of the FORCE ecosystem is established according to the American Nuclear Society?s Nuclear Quality Assurance (NQA-1) program [American Society of Mechanical Engineers 1982], with specific levels of software quality assurance (SQA) within NQA-1 applied to each software tool in FORCE. As the tools within FORCE have matured, some integration algorithms to accurately connect the software tools for holistic analysis have been developed and deployed within the FORCE software repository. In accordance with NQA-1 standards, regression tests are required to guarantee the software performs consistently even when new capabilities are added to the software. In this report, we document the deployment of both unit tests, which test the consistent behavior of small pieces of the FORCE code base, as well as integration tests, which test the consistent performance of full use cases for the FORCE integration algorithms. We further document the encapsulation of these tests within a test harness, which collectively checks for each successful test completion on demand. Finally, we document the automation of the test harness using GitHub Actions [GitHub 2024], which require all tests succeed before any new capability or other changes can be added to the FORCE integration software
Climate policies designed to achieve climate change objectives must consider radiative forcing from the Kyoto greenhouse gas, as well as other forcing constituents, such as aerosols and tropospheric ozone. Net positive forcing leads to global average temperature increases. Modeling of non-Kyoto forcing is a relatively new component of climate management scenarios. Five of the nineteen models in the EMF-27 Study model both Kyoto and non-Kyoto forcing. This paper describes and assesses current non-Kyoto radiative forcing modeling within these integrated assessment models. The study finds negative forcing from aerosols masking significant positive forcing in reference non-climate policy projections. There are however large differences across models in projected non-Kyoto emissions and forcing, with differences stemming from differences in relationships between Kyoto and non-Kyoto emissions and fundamental differences in modeling structure and assumptions. Air pollution and non-Kyoto forcing decline in the climate policy scenarios. However, non-Kyoto forcing appears to be influencing mitigation results, including allowable carbon dioxide emissions, and further evaluation is merited. Overall, there is substantial uncertainty related to non-Kyoto forcing that must be considered.
Direct measurement of the forces experienced by micro-spheres in an acoustic standing wave device have been obtained using calibrated optical traps generated with holographic optical tweezers. A micro-sphere, which is optically trapped in three dimensions, can be moved through the acoustic device to measure forces acting upon it. When the micro-sphere is subjected to acoustic forces, it's equilibrium position is displaced to a position where the acoustic forces and optical forces are balanced. Once the optical trapping stiffness has been calibrated, observation of this displacement enables a direct measurement of the forces acting upon the micro-sphere. The measured forces are separated into a spatially oscillating component, attributed to the acoustic radiation force, and a constant force, attributed to fluid streaming. As the drive conditions of the acoustic device were varied, oscillating forces (>2.5 pN{sub pp}) and streaming forces (<0.2 pN) were measured. A 5 μm silica micro-sphere was used to characterise a 6.8 MHz standing wave, λ = 220 μm, to a spatial resolution limited by the uncertainty in the positioning of the micro-sphere (here to within 2 nm) and with a force resolution on the order of 10 fN. The results have application in the design and testing of acoustic manipulation devices.