Search NASASearch

SEARCH · Search NASA

Results for “Sensitivity”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Unveiling Highly Sensitive Active Site in Atomically Dispersed Gold Catalysts for Enhanced Ethanol Dehydrogenation

Developing a desirable ethanol dehydrogenation process necessitates a highly efficient and selective catalyst with low cost. Herein, we show that the “complex active site” consisting of atomically dispersed Au atoms with the neighboring oxygen vacancies (Vo) and undercoordinated cation on oxide supports can be prepared and display unique catalytic properties for ethanol dehydrogenation. The “complex active site” Au-Vo-Zr 3+ on Au 1 /ZrO 2 exhibits the highest H 2 production rate, with above 37,964 mol H 2 per mol Au per hour (385 g H 2 $g^{-1}_{Au}$ h -1 ) at 350 °C, which is 3.32, 2.94 and 15.0 times higher than Au 1 /CeO 2 , Au 1 /TiO 2 , and Au 1 /Al 2 O 3 , respectively. Combining experimental and theoretical studies, we demonstrate the structural sensitivity of these complex sites by assessing their selectivity and activity in ethanol dehydrogenation. Our study sheds new light on the design and development of cost-effective and highly efficient catalysts for ethanol dehydrogenation. Fundamentally, atomic-level catalyst design by colocalizing catalytically active metal atoms forming a structure-sensitive “complex site”, is a crucial way to advance from heterogeneous catalysis to molecular catalysis. In conclusion, our study advanced the understanding of the structure sensitivity of the active site in atomically dispersed catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Incorporating geological structure into sensitivity analysis of subsurface contaminant transport

Simulating subsurface contaminant transport at the kilometer-scale often entails modeling reactive flow and transport within and through complex geologic structures. These structures are typically meshed by hand and as a result geologic structure is usually represented by one or a few deterministically generated geological models for uncertainty studies of flow and transport in the subsurface. Uncertainty in geologic structure can have a significant impact on contaminant transport. In this study, the impact of geologic structure on contaminant tracer transport in a shale formation is investigated for a simplified generic deep geologic repository for permanent disposal of spent nuclear fuel. An open-source modeling framework is used to perform a sensitivity analysis study on transport of two tracers from a generic spent nuclear fuel repository with uncertain location of the interfaces between the stratum of the geologic structure. The automated workflow uses sampled realizations of the geological structural model in addition to uncertain flow parameters in a nested sensitivity analysis. Concentration of the tracers at observation points within, in line with, and downstream of the repository are used as the quantities of interest for determining model sensitivity to input parameters and geological realization. Finally, the results of the study indicate that the location of strata interfaces in the geological structure has a first-order impact on tracer transport in the example shale formation, and that this impact may be greater than that of the uncertain flow parameters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation

Validation and moisture content sensitivity analysis of cross-laminated timber wall assemblies in EnergyPlus

Cross-laminated timber buildings are becoming more common in North America, with many numerical studies showing potential energy savings. However, no studies have validated any EnergyPlus heat transfer algorithms or quantified their accuracy in simulating CLT in building envelopes. This study empirically validates the heat flux predictions for each of EnergyPlus's heat transfer algorithms (Conduction Transfer Functions (CTF), Effective Moisture Penetration Depth (EMPD), Conduction Finite Difference (CondFD), and Heat and Moisture Transfer (HAMT)) for two different CLT ply thicknesses with both summer and winter boundary conditions measured in controlled lab experiments. It also evaluates the model sensitivity of heat flux and heating and cooling loads to moisture content. The 1D validation shows that the HAMT model is the most accurate among all algorithms. All EnergyPlus's heat flux predictions are accurate independent of CLT plate thickness for summer conditions. However, the three constant property algorithms (CTF, EMPD, and CondFD) underpredict heat flux throughout the whole day during winter conditions. The 1D sensitivity analysis indicates that elevated moisture content can increase peak heat fluxes through the material by up to 20 %. Finally, the whole building model sensitivity analysis shows increased heating load and slight cooling load variation due to increased moisture content when using constant property models. The analysis shows significantly lower peak thermal demand (7 % lower heating and 6 % lower cooling) and monthly thermal load (8 % less cooling and 6 % less heating) predictions when using HAMT vs a constant property model.

42 ENGINEERING

DNA Origami Incorporated into Solid-State Nanopores Enables Enhanced Sensitivity for Precise Analysis of Protein Translocations

The rapidly advancing field of nanotechnology is driving the development of precise sensing methods at the nanoscale, with solid-state nanopores emerging as promising tools for biomolecular sensing. Here, this study investigates the increased sensitivity of solid-state nanopores achieved by integrating DNA origami structures, leading to the improved analysis of protein translocations. Using holo human serum transferrin (holo-hSTf) as a model protein, we compared hybrid nanopores incorporating DNA origami with open solid-state nanopores. Results show a significant enhancement in holo-hSTf detection sensitivity with DNA origami integration, suggesting a unique role of DNA interactions beyond confinement. This approach holds potential for ultrasensitive protein detection in biosensing applications, offering advancements in biomedical research and diagnostic tool development for diseases with low-abundance protein biomarkers. Further exploration of origami designs and nanopore configurations promises even greater sensitivity and versatility in the detection of a wider range of proteins, paving the way for advanced biosensing technologies.

77 NANOSCIENCE AND NANOTECHNOLOGY

An Antibody Cocktail-Based Immunoaffinity-LC-MS Method Enabled Ultra-Sensitive and Robust Quantification of Circulating Proinsulin Proteoforms and C-Peptide

Accurately measuring circulating proinsulin proteoforms is crucial for clinical investigation of diabetes, but was previously not feasible owing to limited assay specificity/sensitivity. Here, in this study, we devised a highly sensitive LC-MS-based strategy to quantify intact proinsulin, des-31,32 and des-64,65 proinsulin, and C-peptide in circulation. The method involves: (i) quantitative, robust affinity capture using an optimized antibody cocktail, eliminating the severe quantitative bias across multiple proteoforms typically introduced when using a single antibody; (ii) Lys-C digestion producing unique signature peptides for each proteoform, and (iii) trapping-nano-LC coupled with FAIMS/dCV-MS for an ultrasensitive analysis. The selective trapping/delivery ensured sensitive/selective analysis of the targets while achieving excellent analytical robustness that is critical for clinical assays, and the FAIMS/dCV substantially reduces baseline noise/interferences, further enhancing S/N. The assay achieved exceptional sensitivity, with serum LOQs of 1.7, 2.3, and 3.6 pg/mL respectively for intact-proinsulin, des-31,32 and des-64,65, representing the first assay capable of sensitively quantifying these major circulating proinsulin proteoforms. We applied this assay to 78 subjects, including autoantibody positive (n = 20) and new-onset type 1 diabetes (T1D, n = 19) with respective age/sex/BMI-matched controls, enabling the first accurate profiling of proinsulin proteoforms in clinical groups. The assay results demonstrated a clear separation of control and new-onset T1D groups that a parallel total-proinsulin ELISA assay fails to capture. Furthermore, distinct expression patterns in relative abundance ratios among proteoforms were observed across clinical groups. This assay may provide valuable insights into the β-cell functions and the onset/progression of diabetes and other associated conditions. Moreover, the strategy is broadly applicable to targeted measurement of other biomarker proteoforms.

Shen, Qingqing [University at Buffalo, NY (United

A Unified Workflow for Sensitivity-Based Kinetic Analysis in Microkinetic Models

Degrees of rate control (DRC), apparent activation energies, and apparent reaction orders are established local sensitivity diagnostics for interpreting microkinetic models, but applying them routinely to large mechanisms often requires substantial reaction-specific bookkeeping, perturbation design, and postprocessing. Here, in this study, we present a unified derivative-based workflow that evaluates these quantities from a single compiled reaction-network model and target-rate definition. For any user-provided microkinetic model, the workflow compiles the mechanism into stoichiometrically consistent mass-action rate equations, solves the surface dynamics, and uses automatic differentiation to compute sensitivities with respect to rate constants, temperature, and gas partial pressures. By combining their calculations in the same framework, the workflow clearly demonstrates the relationships between different DRCs and the apparent activation energy. Using existing examples of propylene partial oxidation and methane oxidation on Pd(100), we verify expected transient redistribution of rate control, distinguish net Campbell DRCs from one-sided directional sensitivities, and show how apparent activation energy can be reconstructed either from one-sided DRCs or from state-based DRCs while critical mechanistic insights are obtained consistently. In the methane oxidation case, a pathway-subset test further illustrates how a simplified mechanism preserves key kinetic signatures of a full model, showing the potential of our user-friendly tool for model construction beyond kinetic analysis.

36 MATERIALS SCIENCE

Enhanced Stability and Sensitivity for CA-125 Detection Under Microfluidic Shear Flow Using Polyethylene Glycol-Coated Biosensor

The microfluidic-based point-of-care (POC) diagnostic tool has garnered significant interest in recent years, offering rapid and cost-effective disease detection. There is a growing trend toward integrating microfluidic platforms with biosensors, aligning lab-on-a-chip technologies with POC diagnostic devices. Despite numerous efforts to incorporate biosensors into microfluidic systems, researchers have performed very limited investigations on the stability of biomarker detection when biosensors operate under microfluidic shear flow conditions. Gold nanoparticles (AuNPs) are a widely employed material in capacitive biosensors for antibody immobilization and sensitivity enhancement. However, AuNPs have limitations in providing stable detection of biomarkers within microfluidic shear flow due to their agglomeration nature. This study addresses these limitations by employing 2 kDa polyethylene glycol (PEG) as an intermediate biofunctional layer to immobilize CA-125 antibodies on gold-interdigitated electrodes for the stable and accurate detection of CA-125 antigens. The stabilities and sensitivities of AuNPs and PEG-coated biosensors are evaluated under both static drop and microfluidic shear flow conditions for CA-125 antigen detection. The experimental results demonstrate a capacitive signal response (5660 pF at 10 kHz) 2.2 times higher using the PEG-coated biosensor than the signal (2551 pF at 10 kHz) measured by the AuNP-coated biosensor in the detection of CA-125 antigen–antibody conjugation under static drop conditions, indicating the higher sensitivity of the PEG-coated biosensor. Additionally, the PEG-coated biosensor exhibits better consistency for the CA-125 antigen detection between static drop and microfluidic shear flow conditions (Cp decrease in percentage (ΔCp%↓) = 2.9% at 10 kHz) compared to the electrical signals measured using the AuNP-coated biosensor (ΔCp%↓ = 32.4% at 10 kHz), which suggests that the PEG-coated biosensor demonstrates higher stability for CA-125 antigen detection under microfluidic shear flow conditions. With these significant improvements brought by the PEG-coated biosensor, especially under microfluidic conditions, a substantial hurdle in developing electrical biosensors for POC diagnostic applications has been overcome, expediting further advancements in the field.

36 MATERIALS SCIENCE

Informing Robust Functional Relationship Benchmarks: An Evaluation of the Temperature Sensitivity of Ecosystem Respiration Across the Arctic-Boreal Region

During land model development, simulated carbon dynamics are often benchmarked against observational data sets to evaluate model performance. Functional relationship benchmarks are the relationship between a driving variable (e.g., temperature) and a response variable (e.g., ecosystem respiration) and are a promising tool for assessing model performance by evaluating modeled sensitivities to changing environmental conditions. However, observed functional relationships can be influenced by choices made during data collection and throughout the benchmarking process, impacting the inferred skill of land models. To avoid misrepresenting a model's true performance, it is necessary to systematically evaluate best practices when constructing functional relationship benchmarks. We developed a set of guidelines for constructing functional relationship benchmarks, considering the choice of data set, number of daily observations, temporal extent, and temporal resolution across Alaska and Canada over a 20-year period from 2001 to 2020. The temperature sensitivity of ecosystem respiration from observations, evaluated through an apparent Q 10 , is highly variable both spatially and as a result of the data processing approach applied in the benchmark formation. When benchmarking 13 models from the Warming Permafrost Model Intercomparison Project (WrPMIP), the range in inferred model skill is substantially impacted by the choices applied in constructing functional relationship benchmarks. The inferred performance of a given model is most sensitive to the number of daily observations and temporal extent, followed by choice of benchmark data set and temporal averaging. Results from this analysis can guide the development of consistent and robust functional relationships for future model evaluation studies.

Poe, Jeralyn [Northern Arizona University, Flagsta

Enhanced sensitivity for electron affinity measurements of rare elements

The electron affinity (EA), the energy released when a neutral atom binds an additional electron, is a fundamental property of atoms that is governed by electron-electron correlations and is strongly related to an element’s chemical reactivity. However, conventional techniques for EA determination lack the experimental sensitivity to probe very scarce samples. As a result, the EA for the heaviest elements of the periodic table is entirely uncharted. Here, we present a novel technique to determine EAs through Laser Photodetachment Threshold Spectroscopy, performed in an electrostatic ion beam trap to increase the samples’ exposure to laser photons and, thus, improve the experimental signal sensitivity by three orders of magnitude. Moreover, the additional exposure time allows the use of lower-power continuous-wave narrow-band lasers that reduce uncertainties associated with broadening effects induced by the laser bandwidth. By applying this technique, we measure the EA of 35 Cl to be 3.612720(44) eV, achieving state-of-the-art precision while employing five orders of magnitude fewer anions. The demonstrated sensitivity paves the way for systematic EA measurements across isotopic chains - including isotope shifts and hyperfine splittings - and ultimately for the first direct determination of electron affinities in superheavy elements.

Maier, F. M. [Univ. of Greifswald (Germany); Europ

DarkSide-20k sensitivity to light dark matter particles

The dual-phase liquid argon time projection chamber is presently one of the leading technologies to search for dark matter particles with masses below 10 GeV c$^{−2}$. This was demonstrated by the DarkSide-50 experiment with approximately 50 kg of low-radioactivity liquid argon as target material. The next generation experiment DarkSide-20k, currently under construction, will use 1,000 times more argon and is expected to start operation in 2027. Based on the DarkSide-50 experience, here we assess the DarkSide-20k sensitivity to models predicting light dark matter particles, including Weakly Interacting Massive Particles (WIMPs) and sub-GeV c$^{−2}$ particles interacting with electrons in argon atoms. With one year of data, a sensitivity improvement to dark matter interaction cross-sections by at least one order of magnitude with respect to DarkSide-50 is expected for all these models. A sensitivity to WIMP–nucleon interaction cross-sections below 1 × 10$^{−42}$ cm$^{2}$ is achievable for WIMP masses above 800 MeV c$^{−2}$. With 10 years exposure, the neutrino fog can be reached for WIMP masses around 5 GeV c$^{−2}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Visible-light H 2 evolution using dye-sensitized TiO 2 : effects of physicochemical properties of TiO 2 on excited carrier dynamics and activity

Dye-sensitized photocatalysts have emerged as promising materials for solar-driven water splitting due to their ability to utilize visible light, in contrast to conventional wide-band-gap semiconductors. However, the relationship between semiconductor properties and charge carrier dynamics remains insufficiently understood. In this study, we investigated Pt/TiO 2 systems sensitized with a visible-light-absorbing Ru(II) polypyridyl complex (RuP), focusing on how the crystal phase and specific surface area of TiO 2 influence excited carrier dynamics and H 2 evolution activity. To isolate the effects of TiO 2 properties, Pt and RuP loadings were standardized across samples. Emission lifetime analysis showed similarly efficient electron injection from RuP to TiO 2 in all cases, suggesting that injection efficiency does not account for observed differences in activity. Transient absorption measurements revealed that back electron transfer (BET) rates depended strongly on the TiO 2 phase, with anatase and P25 exhibiting slower BET and higher activity for H 2 evolution than rutile. The highest apparent quantum yield for H 2 evolution was 12.0% at 450 nm. Among anatase samples, larger surface areas correlated with higher activity, while smaller-area samples exhibited slower BET rates but still low H 2 evolution activity, implying a role for RuP dye–dye interactions in performance loss. This was further supported by improvements in H 2 evolution activity by lowering RuP loading or adding co-adsorbents. Overall, these results demonstrate that both BET suppression and control over RuP dye aggregation are essential for designing efficient dye-sensitized photocatalytic systems.

Harada, Kakeru [Institute of Science Tokyo (Japan)

Relative sensitivity of plastic scintillator: A comparative analysis with 60 Co gamma rays, deuterium–deuterium, and deuterium–tritium neutrons

A plastic scintillator has found extensive application in the realm of high-energy physics and national security science. Many applications in those fields often involve the simultaneous production of photons, neutrons, and charged particles, which makes the relative sensitivity information for these different radiation types important. In this study, we have adopted a multi-head detector comprised of a plastic scintillator and high gain phototubes, which provides a large dynamic range and linearity. A comparative study on the relative sensitivities of plastic scintillators was facilitated by adopting three distinct radiation calibration sources (i.e., 60 Co γ rays, DD neutrons, and DT neutrons). Neutrons from a DD source generate a comparable level of scintillation to gamma rays emitted by 60 Co (i.e., 60 Co-γ/DD-n = 0.92 ± 16%). DT neutrons induce ~3.5 times the scintillation observed with DD neutrons (i.e., DT-n/DD-n = 3.5 ± 28%). In addition, the Geant4 simulation granted us valuable insights into the relative sensitivity of the scintillator. This comparative study will provide a useful database for users in diverse applications.

47 OTHER INSTRUMENTATION

SPECTER: an instrument concept for CMB spectral distortion measurements with enhanced sensitivity

Deviations of the cosmic microwave background (CMB) energy spectrum from a perfect blackbody uniquely probe a wide range of physics, ranging from fundamental physics in the primordial Universe (μ-distortion) to late-time baryonic feedback processes (y-distortion). While the y-distortion can be detected with a moderate increase in sensitivity over that of COBE/FIRAS, the ΛCDM-predicted μ-distortion is roughly two orders of magnitude smaller and requires substantial improvements, with foregrounds presenting a serious obstacle. Within the standard model, the dominant contribution to μ arises from energy injected via Silk damping, yielding sensitivity to the primordial power spectrum at wavenumbers k ≈ 1-10 4 Mpc -1 . Here, we present a new instrument concept, SPECTER, with the goal of robustly detecting μ. The instrument technology is similar to that of LiteBIRD, but with an absolute temperature calibration system. Using a Fisher approach, we optimize the instrument's configuration to target μ while marginalizing over foreground contaminants. Unlike Fourier-transform-spectrometer-based designs, the specific bands and their individual sensitivities can be independently set in this instrument, allowing significant flexibility. We forecast SPECTER to observe the ΛCDM-predicted μ-distortion at ≈ 5σ (10σ) assuming an observation time of 1 (4) year(s) (corresponding to mission duration of 2 (8) years), after foreground marginalization. Our optimized configuration includes 16 bands spanning 1–2000 GHz with ∼degree-scale angular resolution at ∼ 150 GHz and 1100 total detectors. SPECTER will additionally measure the y-distortion at sub-percent precision and its relativistic correction at percent-level precision, yielding tight constraints on the total thermal energy and mean temperature of ionized gas.

CMBR experiments

Future projections of storm surge in Hurricane Katrina and sensitivity to meteorological forcing resolution

In this study, we investigated whether and how the storm surge induced by Hurricane Katrina could change if it occurs in a future warmer climate, and the sensitivity of the changes to atmospheric forcing resolution. Climate model simulations of Hurricane Katrina at 27 km, 4.5 km, and 3 km resolutions were used to drive storm surge simulations in historical and future climates using the ADvanced CIRCulation (ADCIRC) model. We found that peak surge height increased significantly in the future with all forcing resolutions. However, the future projection is 22% greater in the 3 km forcing, typical of regional climate models, compared to the 27 km forcing, typical of state-of-the-art global climate models. Additionally, the spatial extent of the future change is highly sensitive to forcing resolution, extending most broadly under the 27 km forcing. Furthermore, we found that storm surge duration decreases in the future with all forcing resolutions due to increasing TC translation speed and decreasing ocean lifetime. However, the future change in the surge duration is sensitive to the forcing resolution, decreasing by 31% in the 27 km forcing and 6% in the 3 km forcing.

54 ENVIRONMENTAL SCIENCES

Sensitivity of nEXO to 136 Xe charged-current interactions: Background-free searches for solar neutrinos and fermionic dark matter

We study the sensitivity of nEXO to solar neutrino charged-current interactions, 𝜈 𝑒 + 136 Xe → 136 Cs*+𝑒 − , as well as analogous interactions predicted by models of fermionic dark matter. Due to the recently observed low-lying isomeric states of 136 Cs, these interactions will create a time-delayed coincident signal observable in the scintillation channel. Here we develop a detailed Monte Carlo simulation of scintillation emission, propagation, and detection in the nEXO detector to model these signals under different assumptions about the timing resolution of the photosensor readout. We show this correlated signal can be used to achieve background discrimination on the order of 10 −9 , enabling nEXO to make background-free measurements of solar neutrinos above the reaction threshold of 0.668 MeV. We project that nEXO could measure the flux of neutrinos from the carbon-nitrogen-oxygen cycle with a statistical uncertainty of 25%, thus contributing a novel and competitive measurement toward addressing the solar metallicity problem. Additionally, nEXO could measure the mean energy of the 7 Be neutrinos with a precision of 𝜎 ≤ 1.5 keV and could determine the survival probability of 7 Be and pep solar 𝜈𝑒 with precision comparable to the state of the art. These quantities are sensitive to the Sun’s core temperature and to nonstandard neutrino interactions, respectively. Here, the strong background suppression would allow nEXO to search for charged-current interactions of fermionic dark matter in the mass range 𝑚 𝜒 = 0.668–7 MeV with a sensitivity up to three orders of magnitude better than current limits.

47 OTHER INSTRUMENTATION

Demonstration of x-ray fluorescence spectroscopy as a sensitive temperature diagnostic for high-energy-density physics experiments

We present the use of x-ray fluorescence spectroscopy (XFS) to a sensitive temperature diagnostic in shocked foams at temperatures of 30–75 eV. Cobalt-doped foams were shock compressed using a planar drive at the OMEGA laser facility and photo-pumped with a Zn He⁢𝛼 x-ray source. Analysis of the resulting cobalt 𝐾⁢𝛽 x-ray fluorescence spectra using collisional radiative codes allows the temperature to be determined in the shocked foams. Furthermore, this method provides a sensitive and robust technique to determine temperatures in high-energy-density physics experiments in the tens of electronvolts temperature range. In these experiments, we find that radiation hydrodynamic simulations predict a lower temperature in the shocked foams compared to analysis of the XFS data using collisional radiative models. Although additional experiments with an independent temperature diagnostic to absolutely calibrate XFS spectra for these conditions will be required to resolve this discrepancy, these results demonstrate the excellent temperature sensitivity of XFS spectra for high-energy-density physics experiments.

Atomic spectra

Universal time scalings of sensitivity in Markovian quantum metrology

Assuming Markovian time evolution of a quantum sensing system, we study the general characterization of the optimal sensitivity scalings with time, under most general quantum control protocols. We allow the estimated parameter to influence both the Hamiltonian as well as the dissipative part of the quantum master equation and focus on the asymptotic-time along with the short-time sensitivity scalings. We find that via simple algebraic conditions (in terms of the Hamiltonian, the jump operators as well as their parameter derivatives), one can characterize the four classes of metrological models that represent: quadratic-linear, quadratic-quadratic, linear-linear, and linear-quadratic time scalings. We also investigate the relevant time scales on which the transition between the two regimes appears. Additionally, we provide universal numerical methods to obtain quantitative bounds on sensitivity that are the tightest that exist in the literature. Simplicity and universality of our results make it suitable for diverse applications in quantum metrology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC