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At least 1,189 records · Page 66

The Spatial Standard Observer

The spatial standard observer is a computational model that provides a measure of the visibility of a target in a uniform background image or of the visual discriminability of two images. Standard observers have long been used in science and industry to quantify the discriminability of colors. Color standard observers address the spectral characteristics of visual stimuli, while the spatial standard observer (SSO), as its name indicates, addresses spatial characteristics. The SSO is based on a model of human vision. The SSO was developed in a process that included evaluation of a number of earlier mathematical models that address optical, physiological, and psychophysical aspects of spatial characteristics of human visual perception. Elements of the prior models are incorporated into the SSO, which is formulated as a compromise between accuracy and simplicity. The SSO operates on a digitized monochrome still image or on a pair of such images. The SSO consists of three submodels that operate sequentially on the input image(s): 1. A contrast model, which converts an input monochrome image to a luminance contrast image, wherein luminance values are expressed as excursions from, and normalized to, a mean; 2. A contrast-sensitivity-filter model that includes an oblique-effect filter (which accounts for the decline in contrast sensitivity at oblique viewing angles); and 3. A spatial summation model, in which responses are spatially pooled by raising each pixel to the power beta, adding the results, and raising the sum to the 1/b power. In this model, b=2.9 was found to be a suitable value. The net effect of the SSO is to compute a numerical measure of the perceptual strength of the single image, or of the visible difference (denoted the perceptual distance) between two images. The unit of a measure used in the SSO is the just noticeable difference (JND), which is a standard measure of perceptual discriminability. A target that is just visible has a measure of 1 JND.

Watson, Andrew B.↗

Evaluating large scale aqueous organic redox flow battery performance with a hybrid numerical and machine learning framework

Aqueous organic redox flow battery (AORFB) is a promising cost-competitive technology for large-scale energy storage. Among existing work, the dihydroxyphenazine (DHP)-based AORFB has demonstrated high energy density and low-capacity degradation in 10 cm$^2$ cells during lab tests. However, its commercial-scale performance in more complex environments remains unknown, posing a barrier to commercialization. To address this gap, this work presents a comprehensive performance evaluation of a 780 cm$^2$ DHP-based AORFB by combining a physics-based numerical model, machine learning (ML)-based surrogate models, and ML-derived sensitivity quantification. Specifically, we first select 12 key battery parameters that include 10 physicochemical and 2 operation quantities, then select 6 performance metrics that include energy efficiency (EE), discharging capacity, charging energy, and power losses due to concentration, activation, and ohmic over-potentials. With such selection, 12800 combinations of the 12 parameters are subsequently generated using the Latin Hypercube Sampling method. Such combinations, together with 38 pre-defined State of Charge, are then integrated to a validated AORFB model developed in COMSOL to compute the performance metrics. With both input parameters and performance metrics, 60 deep neural network (DNN) surrogate models are then trained to approximate the relationship between the 10 physicochemical quantities and 6 performance metrics at each flow rate and current density. Sensitivity scores are then calculated based on the DNN models. Two additional sensitivity analysis tools, i.e., MARS, and SHAP, are also used to cross-validate the sensitivity scores from the DNN. The results demonstrate that 1) the standard potential ranks first in controlling EE and charging energy, 2) the membrane conductivity is most critical for power loss and EE, and 3) specific area and reaction rate control activation power loss.

25 ENERGY STORAGE↗

Sensitivity Analysis of Drivers Water Shortage in the Los Angeles Region During Drought

The code and detailed step-by-step instructions for generating the model output data, processing results, and analysis and plotting are provided at https://github.com/IMMM-SFA/Ferencz_et_al_2026_ER_Water. The PyArtes model is a python adaptation of the Artes model. PyArtes uses many of the same input data and optimization model architecture as Artes. Documentation for the PyArtes model is provided in the Supplement to the paper. The primary data product are simulated monthly water shortages for indoor and outdoor demand under a large ensemble of drought scenarios (>13,000). The droughts are hypothetical and are not based on historical time series data of supply sources - though historical data did help inform ranges explored for supply parameters. Demands are informed by recent 2017-2021 water supply data. Demands used for the model can be accessed at https://github.com/IMMM-SFA/Ferencz_et_al_2026_ER_Water. Simulations resolve demand for over 90 water providers in the study region. The results report 36 months of water shortage data for each indoor and outdoor demand node. The study also developed a multilayer perceptron (MLP) neural network trained on a subset of the simulated shortage ensemble to emulate worst annual water shortage for a given set of parameter multipliers -- provided the parameter values fall within the ranges sampled in the ensemble. Emulated water shortages for synthetic ensembles are in the MLP-generated shortages folder. The MLP model was used to generate larger ensembles to support Sobol analysis that would have been extremely computationally expensive to simulate. Datasets provided in this repository*: Simulated shortages. These results are used for the analysis for Figures 5, 8, and 9 in the paper, and also to train the MLP emulator. .zip file containing outputs for the 13,312 scenario ensemble. Separate .csv files for indoor and outdoor shortage for each scenario. Rows = demand ids (~100), Columns = months (36) Units = acre-feet/month of shortage (shortage = monthly demand - supply). 1 acft = 1233.48 m^3 .csv files of aggregated shortages derived from the 13,312 ensemble Rows = scenarios (13,312), Columns = demand ids (~100) Units = acre-feet/year (either worst annual shortage or total shortage over the 3-year drought) .csv file of the parameter multipliers scenarios for the ensemble .csv file of the parameter ranges and baseline values the multipliers were applied to MLP-generated shortages. These results are used for Figures 4, 6, and 7 in the paper. mwd higher folder: scenario ensembles, emulated worst year total shortages (acft), and Sobol results Emulated shortages. Rows = scenarios, columns = demand ids, units acft Sobol results. Rows = demand ids, columns Sobol (S1, ST, or 95% confidence interval) value for each parameter mwd lower folder: scenario ensembles, emulated worst year total shortages (acft), and Sobol results same organization as mwd higher MLP performance: performance metrics (R^2, RMSE, BIAS, MAPE) for the testing subset (20% or 2,662 scenarios) and simulated vs emulated worst year shortage (acre-feet/year) for every demand node, MWD wholesale regions, and the entire study region (LAC). Supporting data for figures. Figure plotting scripts in the associated GitHub repo. These files support analysis and visualization. Geospatial Data used for plotting simulated water shortages and Sobol results. Dictionary of full names for demand nodes in the model and estimates of water supply by source type informed by Artes input files and California Urban Water Management Planning data: https://water.ca.gov/Programs/Water-Use-And-Efficiency/Urban-Water-Use-Efficiency/Urban-Water-Management-Plans *Readme files provided for each folder.

drought↗

User Manual for Whisper-1.1

Whisper is a statistical analysis package developed in 2014 to support nuclear criticality safety (NCS) validation [1-3]. It uses the sensitivity profile data for an application as computed by MCNP6 [4-6] along with covariance files [7,8] for the nuclear data to determine a baseline upper-subcritical-limit (USL) for the application. Whisper version 1.0 was first developed and used at LANL in 2014 [3]. During 2015- 2016, Whisper was updated to version 1.1 and is to be included with the upcoming release of MCNP6.2. This document describes the user input and options for running whisper-1.1, including 2 perl utility scripts that simplify ordinary NCS work, whisper_mcnp.pl and whisper_usl.pl. For many detailed references on the theory, applications, nuclear data & covariances, SQA, verification-validation, adjointbased methods for sensitivity-uncertainty analysis, and more – see the Whisper – NCS Validation section of the MCNP Reference Collection at mcnp.lanl.gov. There are currently over 50 Whisper reference documents available.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A hybrid numerical and machine learning framework for evaluating the performance of a 780 cm 2 aqueous organic redox flow battery

Aqueous organic redox flow battery (AORFB) is a promising cost-competitive technology for large-scale energy storage. Among existing work, the dihydroxyphenazine (DHP)-based AORFB has demonstrated high energy density and low capacity degradation in 10 cm2 cells during lab tests. However, its commercial-scale performance in more complex environments remains unknown, posing a barrier for commercialization. To address this gap, this work presents a comprehensive performance evaluation of a 780 cm 2 DHP-based AORFB by combining physics-based numerical model, machine learning (ML)-based surrogate models, and ML-derived sensitivity quantification. Specifically, we first select 12 key battery parameters that include 10 physicochemical quantities and 2 operation quantities, then select 6 performance metrics that include energy efficiency (EE), discharging capacity, charging energy, and power losses due to concentration, activation, and ohmic over-potentials. With such selection, 12800 combinations of the 12 parameters are subsequently generated using the Latin Hypercube Sampling method. These combinations, together with 38 pre-defined State of Charge, are then integrated to a validated AORFB model developed in COMSOL to compute the performance metrics. With both input parameters and performance metrics, 60 deep neural network (DNN) surrogate models are then trained to approximate the relationship between the 10 physicochemical quantities and 6 performance metrics at each flow rate and current density. Sensitivity scores are then calculated based on the DNN models. Two additional sensitivity analysis tools, i.e., MARS, and SHAP, are also used to cross-validate the sensitivity scores from the DNN. The results demonstrate that 1) the standard potential ranks the first in controlling EE and charging energy, 2) the membrane conductivity is most critical for power loss and EE, and 3) specific area and reaction rate control activation power loss.

25 ENERGY STORAGE↗

Adaptive sparse polynomial dimensional decomposition for derivative-based sensitivity

In this report applications, such as the plasma-coupled combustion system we consider, derivative-based sensitivity indices (DSI) are known to have several advantages over Sobol's total sensitivity indices, especially for small sample sizes. Several properties of derivative-based sensitivity measures are leveraged to develop a new and efficient numerical approach to estimate them. It is based on computing the DSI measures by effectively cost-free Monte Carlo sampling of an adaptively constructed orthogonal polynomial surrogate with uncertain input parameters that can have arbitrary probability distributions. The adaptivity reduces the number of necessary model evaluations, which is demonstrated both in a constructed example (the Moon function) and in two plasma-combustion systems with up to 55 uncertain parameters. Unimportant parameters are successfully identified and neglected with a low number of model evaluations, which makes it an attractive non-intrusive approach when adjoint solutions are unavailable to provide sensitivity information.

42 ENGINEERING↗

The Primordial Inflation Explorer (PIXIE)

The Primordial Inflation Explorer is an Explorer-class mission to measure the gravity-wave signature of primordial inflation through its distinctive imprint on the linear polarization of the cosmic microwave background. PIXIE uses an innovative optical design to achieve background-limited sensitivity in 400 spectral channels spanning 2.5 decades in frequency from 30 GHz to 6 THz (1 cm to 50 micron wavelength). Multi-moded non-imaging optics feed a polarizing Fourier Transform Spectrometer to produce a set of interference fringes, proportional to the difference spectrum between orthogonal linear polarizations from the two input beams. The differential design and multiple signal modulations spanning 11 orders of magnitude in time combine to reduce the instrumental signature and confusion from unpolarized sources to negligible levels. PIXIE will map the full sky in Stokes I, Q, and U parameters with angular resolution 2.6 deg and sensitivity 0.2 uK per 1 deg square pixel. The principal science goal is the detection and characterization of linear polarization from an inflationary epoch in the early universe, with tensor-to-scalar ratio r <10(exp -3) at 5 standard deviations. In addition, the rich PIXIE data will constrain physical processes ranging from Big Bang cosmology to the nature of the first stars to the physical conditions within the interstellar medium of the Galaxy. We describe the PIXIE instrument and mission architecture needed to detect the signature of an inflationary epoch in the early universe using only 4 semiconductor bolometers.

Kogut, Alan J.↗

Exoplanet Yield Sensitivity for the Hybrid Lyot Coronagraph from end-to-end modeling for LUVOIR-A

NASA's future direct imaging flagship mission will require telescope mirror segmentation to survey a statistically significant population of nearby stellar systems by increasing aperture size beyond that achieved by traditional space-borne monolithic apertures thus far. Segmentation is a path for the size expansion, but it entails a challenge due to the introduction of temporal pupil discontinuities in terms of both phase and amplitude. Modeling of the integrated performance of the coronagraph with the expected dynamical profile of the telescope is an important step toward realistic estimates of the mission's science yields. We present results of a study using the hybrid Lyot coronagraph with a 15-m on-axis, segmented optical telescope assembly (OTA), akin to that of the Large UV / Optical /Infrared (LUVOIR) mission. We have developed a high-fidelity, end-to-end model as part of the Segmented Coronagraph Design and Analysis (SCDA) study that includes diffractive optical propagations at the 1e-10 contrast level across the optical train including the OTA and intermediate re-imaging optics inside the coronagraph instrument. We perform a sensitivity analysis to assess the contrast sensitivity to wavefront perturbations for a set of key telescope terms including segment-level low-order and mid-spatial frequency aberrations and evaluate expected exoplanet yields obtained in the presence of these sets of aberrations. Industry-provided segment-level wavefront aberration datasets involving the following mechanisms are input to the end-to-end model: (1) thermal gradients and accelerations, and (2) telescope dynamics including line-of-sight and segment jitter. Dynamically averaged PSFs in the presence of aberrations are fed into AYO (Altruistic Yield Optimization), a mission design reference simulator, that then assesses the scientific yield sensitivities.

high-contrast imaging↗

Design tradeoff studies and sensitivity analysis, appendices B1 - B4

Documentation is presented for a program which separately computes fuel and energy consumption for the two modes of operation of a hybrid electric vehicle. The distribution of daily travel is specified as input data as well as the weights which the component driving cycles are given in each of the composite cycles. The possibility of weight reduction through the substitution of various materials is considered as well as the market potential for hybrid vehicles. Data relating to battery compartment weight distribution and vehicle handling analysis is tabulated.

Source record↗

Replicating Machine Learning Experiments in Materials Science

Transparency and reproducibility are important aspects of validation for Machine Learning (ML) models that are not fully understood and applies independently of the application domain.We offer a case study of reproducibility that highlights the challenges encountered when attempting to reproduce analyzes obtained with Machine Learning methods in materials informatics. Our study explores prediction results obtained with ML models and issues in training data serving as input. We discuss challenges related to theory-driven and numerical errors in training data, lack of reproducibility across platforms and versions, and effects of randomness when varying hyperparameters. In addition to model accuracy, a main metric of interest in the ML community, our results show that model sensitivity may be equally important for applying ML in domain applications such a materials science.

97 MATHEMATICS AND COMPUTING↗

Mechanistic Understanding and Rational Design of Quantum Dot/Mediator Interfaces for Efficient Photon Upconversion

The semiconductor-nanocrystal-sensitized, three-component upconversion system has made great strides over the past 5 years. The three components (i.e., triplet photosensitizer, mediator, and emitter) each play critical roles in determining the input and output photon energy and overall quantum efficiency (QE). The nanocrystal photosensitizer converts the absorbed photon into singlet excitons and then triplet excitons via intersystem crossing. The mediator accepts the triplet exciton via either direct Dexter-type triplet energy transfer (TET) or sequential charge transfer (CT) while extending the exciton lifetime. Through a second triplet energy-transfer step from the mediator to the emitter, the latter is populated in its lowest excited triplet state. Triplet–triplet annihilation (TTA) between two triplet emitters generates the emitter in its bright singlet state, which then emits the upconverted photon. Quantum dots (QD) have a tunable band gap, large extinction coefficient, and small singlet–triplet energy losses compared to metal–ligand charge-transfer complexes. This high triplet exciton yield makes QDs good candidates for photosensitizers. In terms of driving triplet energy transfer, the triplet energy of the mediator should be slightly lower than the triplet exciton energy of the QD sensitizer for a downhill energy landscape with minimal energy loss. The same energy cascade is also required for the transfer from the mediator to the emitter. Lastly, the triplet energy of the emitter must be slightly larger than one-half of its singlet energy to ensure that TTA is exothermic. Optimization of the sensitizer, mediator, and emitter will lead to an increase in the anti-Stokes shift and the total quantum efficiency. Evaluating each individual step’s efficiency and kinetics is necessary for the understanding of the limiting factors in existing systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Is infrared-collinear safe information all you need for jet classification?

Machine learning-based jet classifiers are able to achieve impressive tagging performance in a variety of applications in high-energy and nuclear physics. However, it remains unclear in many cases which aspects of jets give rise to this discriminating power, and whether jet observables that are tractable in perturbative QCD such as those obeying infrared-collinear (IRC) safety serve as sufficient inputs. In this article, we introduce a new classifier, Jet Flow Networks (JFNs), in an effort to address the question of whether IRC unsafe information provides additional discriminating power in jet classification. JFNs are permutation-invariant neural networks (deep sets) that take as input the kinematic information of reconstructed subjets. The subjet radius and a cut on the subjet’s transverse momenta serve as tunable hyperparameters enabling a controllable sensitivity to soft emissions and nonperturbative effects. We demonstrate the performance of JFNs for quark vs. gluon and Z vs. QCD jet tagging. For small subjet radii and transverse momentum cuts, the performance of JFNs is equivalent to the IRC-unsafe Particle Flow Networks (PFNs), demonstrating that infrared-collinear unsafe information is not necessary to achieve strong discrimination for both cases. As the subjet radius is increased, the performance of the JFNs remains essentially unchanged until physical thresholds that we identify are crossed. For relatively large subjet radii, we show that the JFNs may offer an increased model independence with a modest tradeoff in performance compared to classifiers that use the full particle information of the jet. These results shed new light on how machines learn patterns in high-energy physics data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Offshore application of landslide susceptibility mapping using gradient-boosted decision trees: a Gulf of Mexico case study

Abstract Among natural hazards occurring offshore, submarine landslides pose a significant risk to offshore infrastructure installations attached to the seafloor. With the offshore being important for current and future energy production, there is a need to anticipate where future landslide events are likely to occur to support planning and development projects. Using the northern Gulf of Mexico (GoM) as a case study, this paper performs Landslide Susceptibility Mapping (LSM) using a gradient-boosted decision tree (GBDT) model to characterize the spatial patterns of submarine landslide probability over the United States Exclusive Economic Zone (EEZ) where water depths are greater than 120 m. With known spatial extents of historic submarine landslides and a Geographic Information System (GIS) database of known topographical, geomorphological, geological, and geochemical factors, the resulting model was capable of accurately forecasting potential locations of sediment instability. Results of a permutation modelling approach indicated that LSM accuracy is sensitive to the number of unique training locations with model accuracy becoming more stable as the number of training regions was increased. The influence that each input feature had on predicting landslide susceptibility was evaluated using the SHapely Additive exPlanations (SHAP) feature attribution method. Areas of high and very high susceptibility were associated with steep terrain including salt basins and escarpments. This case study serves as an initial assessment of the machine learning (ML) capabilities for producing accurate submarine landslide susceptibility maps given the current state of available natural hazard-related datasets and conveys both successes and limitations.

Dyer, Alec S. (ORCID:0000000219813904)↗

Differentiable lagrangian shock hydrodynamics with application to stable shock acceleration of density interfaces

We develop a gradient based optimization approach for the equations of compressible, Lagrangian hydrodynamics and demonstrate how it can be employed to automatically uncover strategies to control hydrodynamic instabilities arising from shock acceleration of density interfaces. Strategies for controlling the Richtmyer-Meshkov instability (RMI) are of great benefit for inertial confinement fusion (ICF) where shock interactions with many small imperfections in the density interface lead to instabilities which rapidly grow over time. These instabilities lead to mixing which, in the case of laser driven ICF, quenches the runaway fusion process ruining the potential for positive energy return. Here, we demonstrate that control of these instabilities can be achieved by optimization of initial conditions with ( > 100) parameters. Optimizing over a large parameter space like this is not possible with gradient-free optimization strategies. This requires computation of the gradient of the outputs of a numerical solution to the equations of Lagrangian hydrodynamics with respect to the inputs. We show that the efficient computation of these gradients is made possible via a judicious application of (i) adjoint methods, the exact formal representation of sensitivities involving partial differential equations, and (ii) automatic differentiation (AD), the algorithmic calculation of derivatives of functions. Careful regularization of multiple operators including artificial viscosity and timestep control is required. We perform design optimization of > 100 parameter energy field driving the Richtmyer Meshkov instability showing significant suppression while simultaneously enhancing the acceleration of the interface relative to a nominal baseline case.

Hydrophysics↗

Ensemble-based flood vulnerability assessment for probable maximum flood in a changing environment

The magnitude and frequency of hydro-meteorological extremes are expected to increase in a changing environment in ways that threaten the security of US energy-water assets. These include probable maximum precipitation (PMP) and probable maximum flood (PMF), which are used as hydraulic design standards for highly sensitive infrastructures such as nuclear power plants and main dams. To assess the flood vulnerability due to PMP/PMF, an integrated high-resolution process-based hydro-meteorologic modeling framework was used to develop ensemble-based probabilistic flood maps based on best-available historic observations and future climate projections. A graphics processing unit–accelerated 2-dimensional hydrodynamic model was used to simulate the surface inundation areas corresponding to a total of 120 PMF hydrographs. These ensemble-based PMF maps were compared with flood maps obtained from the conventional deterministic PMP/PMF approach, revealing added information about conditional probability of flooding. Further, a relative sensitivity test was conducted to explore the effects of various factors in the framework, such as meteorological forcings, antecedent hydrologic conditions, reservoir storage, and flood model input resolution and parameters. In conclusion, the proposed framework better illustrates the uncertainties associated with model inputs, parameterization, and hydro-meteorological factors, allowing more informed decision-making for future emergency preparation.

58 GEOSCIENCES↗

Development of multi-objective core optimization framework and application to sodium-cooled fast test reactors

The optimization of a Sodium-cooled Fast Reactor (SFR) core is a challenging process, due to the large number of design parameters, the nonlinearities among inputs and outputs, and the complicated correlation among output parameters. This study attempts to develop a generalized framework for the SFR core optimization by coupling the sensitivity analysis, advanced optimization algorithm, and optionally the surrogate modeling. The framework is built based on the fast reactor modeling capability of the Argonne Reactor Computation (ARC) suite and the sensitivity analysis and optimization modules embedded in the DAKOTA code, both have been integrated within the NEAMS Workbench. The genetic algorithm is selected as the optimization method for its robustness, while the option of surrogate modeling is also explored to alleviate the computational burden caused by employing the ARC direct core physics simulation and thus enhance the efficiency of the optimization. Finally, the normalized deviations of performance parameters of the near-optimal solution from those of the ideal core are calculated and used as criteria to down select the final core design. The developed framework is applied to the Advanced Burner Test Reactor (ABTR) core, and optimal solutions are determined by balancing various objectives simultaneously, including peak fast flux, core volume, power, reactivity swing, plutonium mass feed, while at the same time satisfying the predefined constraints due to safety or economics considerations. The optimal ABTR core design obtained using the direct physical simulation and surrogated model are compared and discussed. It is found that using the accurately constructed surrogate models can significantly reduce the required computational time while maintaining satisfactory accuracy.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Laser red shifting based characterization of wakefield excitation in a laser-plasma accelerator

Optical spectra of a drive laser exiting a channel guided laser-plasma accelerator (LPA) are analyzed through experiments and simulations to infer the magnitude of the excited wakefields. The experiments are performed at sufficiently low intensity levels and plasma densities to avoid electron beam generation via self-trapping. Spectral redshifting of the laser light is studied as an indicator of the efficiency of laser energy transfer into the plasma through the generation of coherent plasma wakefields. Influences of input laser energy, plasma density, temporal and spatial laser profiles, and laser focal location in a plasma channel are analyzed. Energy transfer is found to be sensitive to details of laser pulse shape and focal location. The experimental conditions for these critical parameters are modeled and included in particle-in-cell simulations. Simulations reproduce the redshift of the laser within uncertainties of the experiments and produce an estimate of the wake amplitudes in the experiments as a function of amount of redshift. The results support the practical use of laser redshifting to quantify the longitudinally averaged accelerating field that a particle would experience in an LPA powered below the self-trapping limit.

43 PARTICLE ACCELERATORS↗

Experimental implementation of a nonlinear beamsplitter based on a phase-sensitive parametric amplifier

Beamsplitters have played an important role in quantum optics experiments. They are often used to split and combine two beams, especially in the construct of an interferometer. In this letter, we experimentally implement a nonlinear beamsplitter using a phase-sensitive parametric amplifier, which is based on four-wave mixing in hot rubidium vapor. Here we show that, despite the different frequencies of the two input beams, the output ports of the nonlinear beamsplitter exhibit interference phenomena. We make measurements of the interference fringe visibility and study how various parameters, such as the intensity gain of the amplifier, the intensity ratio of the two input beams, and the one and two photon detunings, affect the behavior of the nonlinear beamsplitter. It may find potential applications in quantum metrology and quantum information processing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗