Time Dependence Research Articles

Quantum temporal logic and reachability problems of matrix semigroups

We study the reachability problems of a quantum finite automaton. More precisely, we introduce quantum temporal logic (QTL) that specifies the time-dependent behavior of quantum finite automaton by presenting the time dependence of events temporal operators ◊ (eventually) and □ (always) and employing the projections on subspaces as atomic propositions. The satisfiability of QTL formulae corresponds to various reachability problems of matrix semigroups. We prove that the satisfiability problems for □∨impi, ◊□∨impi and □◊∨impi with atomic propositions pi are decidable. This result solves the open problem of Li and Ying 2014. Notably, the decidability of □◊p can be interpreted as a generalization of Skolem-Mahler-Lech's celebrated theorem based on additive number theory. This paper's last part shows how the quantum finite automaton can model the general concurrent quantum programs, which may involve an arbitrary classical control flow.

Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians

We explore non-equilibrium processes in two-dimensional conformal field theories (2d CFTs) due to the growth of operators induced by inhomogeneous and homogeneous Hamiltonians by investigating the time dependence of the partition function, energy density, and entanglement entropy. The non-equilibrium processes considered in this paper are constructed out of the Lorentzian and Euclidean time evolution governed by different Hamiltonians. We explore the effect of the time ordering on entanglement dynamics so that we find that in a free boson CFT and RCFTs, this time ordering does not affect the entanglement entropy, while in the holographic CFTs, it does. Our main finding is that in the holographic CFTs, the non-unitary time evolution induced by the inhomogeneous Hamiltonian can retain the initial state information longer than in the unitary time evolution.

Screened optimally tuned range separated hybrid functional for solvated low bandgap molecular systems.

The description of electronic properties of low bandgap molecular system is often performed by using density functional theory (DFT) and time dependent (TD) DFT calculations with the optimally tuned range-separated hybrid (OT-RSH) functional, as it contains the necessary ingredients to reliably predict charge transfer excitations. However, the range separating parameter (ω) is system-dependent and its optimization, including the chemical environment, is intricate. Refaely-Abramson et al. demonstrated that the gap renormalization in molecular crystals, a ground state property, can be represented by an OT-RSH functional screened by ɛstatic [Phys. Rev. B 88, 081204(R) (2013)], the zero frequency scalar dielectric constant. In this study, we propose the use of an OT-RSH functional screened by the scalar dielectric constant in the high frequency limit (OT-sRSH), ɛ∞, an appropriate constraint for vertical ionization energies or excitations in a dielectric environment. We have performed calculations for S,N-heteroacene derivatives in tetrahydrofuran and dichloromethane. The "unscreened" OT-RSH functional tends to underestimate experimental ionization potentials (IPs) and optical gaps (Egs) by up to 1.5 and 0.5eV, respectively. In contrast, OT-sRSH functional calculations underestimate IPs and Egs by only 0.4 and 0.2eV. We also compared the OT-sRSH results to explicitly solvated OT-RSH functional calculations for oligothiophenes in dioxane, benzene in ammonia, and methylene blue in water. We observe that both the approaches perform similarly for weakly interacting intermolecular systems and deviate for solvent-solute interacting systems, as expected. In conclusion, the OT-sRSH functional can describe molecular systems with environmental polarization effects accurately, a step toward describing realistic molecular systems.

Population Pharmacokinetic Modeling of Adavosertib (AZD1775) in Patients with Solid Tumors.

Adavosertib (AZD1775) is a potent small-molecule inhibitor of Wee1 kinase. This analysis utilized pharmacokinetic data from 8 Phase I/II studies of adavosertib to characterize the population pharmacokinetics of adavosertib in patients (n = 538) with solid tumors and evaluate the impact of covariates on exposure. A nonlinear mixed-effects modeling approach was employed to estimate population and individual parameters from the clinical trial data. The model for time dependency of apparent clearance (CL) was developed in a stepwise manner and the final model validated by visual predictive checks (VPCs). Using an adavosertib dose of 300 mg once daily on a 5 days on/2 days off dosing schedule given 2 weeks out of a 3-week cycle, simulation analyses evaluated the impact of covariates on the following exposure metrics at steady state: maximum concentration during a 21-day cycle, area under the curve (AUC) during a 21-day cycle, AUC during the second week of a treatment cycle, and AUC on day 12 of a treatment cycle. The final model was a linear 2-compartment model with lag time into the dosing compartment and first-order absorption into the central compartment, time-varying CL, and random effects on all model parameters. VPCs and steady-state observations confirmed that the final model satisfied all the requirements for reliable simulation of randomly sampled Phase I and II populations with different covariate characteristics. Simulation-based analyses revealed that body weight, renal impairment status, and race were key factors determining the variability of drug-exposure metrics.

Universal scaling in far-from-equilibrium quantum systems: An equivalent differential approach

Recent progress in out-of-equilibrium closed quantum systems has significantly advanced the understanding of mechanisms behind their evolution toward thermalization. Notably, the concept of nonthermal fixed points (NTFPs)-responsible for the emergence of spatiotemporal universal scaling in far-from-equilibrium systems-has played a crucial role in both theoretical and experimental investigations. In this work, we introduce a differential equation that has the universal scaling associated with NTFPs as a solution. The advantage of working with a differential equation, rather than only with its solution, is that we can extract several insightful properties not necessarily present in the solution alone. How the differential equation is derived allows physical interpretation of the universal exponents in terms of the time dependence of the amplitude of the distributions and their momentum scaling. Employing two limiting cases of the equation, we determined the universal exponents related to the scaling using the distributions near just two momentum values. We established a solid agreement with previous investigations by validating this approach with three distinct physical systems. This consistency highlights the universal nature of scaling due to NTFPs and emphasizes the predictive capabilities of the proposed differential equation. Moreover, under specific conditions, the equation predicts a power-law related to the ratio of the two universal exponents, leading to implications concerning particle and energy transport. This suggests that the observed power-laws in far-from-equilibrium turbulent fluids could be related to the universal scaling due to NTFPs, potentially offering insights into the study of turbulence.

Estimating forest aboveground biomass in tropical forests with Landsat time-series data and recurrent neural network

ABSTRACT The insensitivity and saturation of sensor signals significantly limit the application of Landsat data on estimating biomass in tropical forests with a high level of biomass. The previous studies with single-date Landsat data have lower accuracies in tropical forests compared to boreal and temperate forests. Landsat time-series data provide a promising opportunity to improve the accuracy by enhancing the relationship between Landsat spectral reflectance and forest aboveground biomass with disturbance and recovery dynamics. Compared to the single-date image, Landsat time-series data can capture abrupt spectral changes (e.g. harvesting and fire) and show the regrowth process in forested pixels. However, very limited studies take advantage of Landsat time-series data to estimate aboveground biomass in tropical forests. Recurrent neural networks (RNNs) are powerful deep learning techniques to capture time dependencies in sequence data. However, the application of RNNs in estimating forest biomass has not been explored yet. Therefore, we integrate the long short-term memory network (LSTM) and the fully connected neuron network (FNN) to establish an RNN-FNN model for estimating forest biomass with Landsat time-series imagery and airborne LiDAR data. We compared the proposed model with the commonly used Random Forest model and linear regression model which are implemented with single-date data. The results show that the RNN-FNN model can deal with Landsat time-series sequence data to enhance the relationship between Landsat spectral reflectance and forest aboveground biomass. The proposed model achieves the R2 of 0.63 and RMSE of 25.5 Mg/ha, which significantly outperformed the Random Forest model and linear regression model with Landsat single-date data. This study demonstrates the value of RNN and Landsat time-series imagery in estimating forest biomass for tropical forests.

On the entanglement of co-ordinate and momentum degrees of freedom in noncommutative space

In this paper, we investigate the quantum entanglement induced by phase-space noncommutativity. Both the position–position and momentum–momentum noncommutativity are incorporated to study the entanglement properties of coordinate and momentum degrees of freedom under the shade of oscillators in noncommutative space. Exact solutions for the systems are obtained after the model is re-expressed in terms of canonical variables, by performing a particular Bopp’s shift to the noncommuting degrees of freedom. It is shown that the bipartite Gaussian state for an isotropic oscillator is always separable. To extend our study for the time-dependent system, we allow arbitrary time dependency on parameters. The time-dependent isotropic oscillator is solved with the Lewis–Riesenfeld invariant method. It turns out that even for arbitrary time-dependent scenarios, the separability property does not alter. We extend our study to the anisotropic oscillator, which provides an entangled state even for time-independent parameters. The Wigner quasi-probability distribution is constructed for a bipartite Gaussian state. The noise matrix (covariance matrix) is explicitly studied with the help of Wigner distribution. Simon’s separability criterion (generalized Peres–Horodecki criterion) has been employed to find the unique function of the (mass and frequency) parameters, for which the bipartite states are separable. In particular, we show that the mere inclusion of non-commutativity of phase-space is not sufficient to generate the entanglement, rather anisotropy is important at the same footing. We explore the experimental viability of our result through the computation of extractable work for the current situation.

Energy Barriers for the Spontaneous Magnetization Reversal of the Atomic Co Chains on Pt(664) Surface in the Model with Dzyaloshinskii–Moriya Interaction

The analytical approach has been developed in the framework of the continuous XY-model. This approach allows calculating the spontaneous magnetization reversal time of finite-length atomic chains on the metallic surface. The interaction of the magnetic moments of atoms is described by the classical Hamiltonian, which includes the Heisenberg exchange interaction, the Dzyaloshinskii–Moriya interaction, and the magnetic anisotropy energy. Using the Co/Pt(664) system as an example, it has been shown that the proposed method is in a good agreement with the results of the numerical simulation in the limit of short and long atomic chains. And for atomic chains of intermediate length, it can be used to estimate an upper bound on the spontaneous magnetization reversal time. We obtained the dependences of the spontaneous magnetization reversal time of finite-length Co chains the value of the exchange integral, parameters of the magnetic anisotropy, and also on the value of the projection of the Dzyaloshinskii vector onto the axis perpendicular to the plane containing the magnetic moments of the atoms. It is shown that the proposed method has a wide range of applicability both in terms of temperature and the values of the physical parameters characterizing the magnetic properties of the atomic chains.

Mass transfer at vapor-liquid interfaces of H2O + CO2 mixtures studied by molecular dynamics simulation

Abstract In many industrial applications as well as in nature, the mass transfer of CO2 at vapor-liquid interfaces in aqueous systems plays an important role. In this work, this process was studied on the atomistic level using non-equilibrium molecular dynamics simulations. In a first step, a molecular model of the system water + CO2 was developed that represents both bulk and interfacial equilibrium properties well. This system is characterized by a very large adsorption and enrichment of CO2 at the vapor-liquid interface. Then, non-equilibrium mass transfer simulations were carried out using a method that was developed recently: CO2 is inserted into the vapor phase of a simulation box which contains a liquid slab. Surprising effects are observed at the interface such as a net repulsion of CO2 particles from the interface and a complex time dependence of the amount of CO2 adsorbed at the interface.

Threshold temperature of superfluorescence generation in CuCl quantum dots under resonant excitation of excitons and resonant two-photon excitation of biexcitons.

We studied the threshold temperature of superfluorescence (SF) generation with regard to biexcitons in CuCl quantum dots (QDs) under resonant two-photon excitation of biexcitons and resonant excitation of excitons to demonstrate the influence of initial population densities in the QDs on SF generation. As a result, the threshold temperature under the resonant excitation of excitons was higher than that under the two-photon excitation of biexcitons. This indicates that the high density of excited dots facilitates the rapid establishment of coherence among the dots, overcoming disadvantages of incomplete population inversion and formation process of biexcitons. We performed a theoretical calculation of the time profiles of the biexcitonic emission based on semiconductor luminescence equations. The experimentally obtained temperature dependence of the time profiles was qualitatively reproduced by calculating their dependence on the dephasing rate. In addition, we estimated the temperature dependence of the phase relaxation time of the biexcitons in the CuCl QDs by analyzing the temperature dependence of SF.

S[formula omitted]T-Net: A novel electroencephalogram signals-oriented emotion recognition model

In this paper, a novel skipping spatial–spectral–temporal network (S3T-Net) is developed to handle intra-individual differences in electroencephalogram (EEG) signals for accurate, robust, and generalized emotion recognition. In particular, aiming at the 4D features extracted from the raw EEG signals, a multi-branch architecture is proposed to learn spatial–spectral cross-domain representations, which benefits enhancing the model generalization ability. Time dependency among different spatial–spectral features is further captured via a bi-directional long-short term memory module, which employs an attention mechanism to integrate context information. Moreover, a skip-change unit is designed to add another auxiliary pathway for updating model parameters, which alleviates the vanishing gradient problem in complex spatial–temporal network. Evaluation results show that the proposed S3T-Net outperforms other advanced models in terms of the emotion recognition accuracy, which yields an performance improvement of 0.23% , 0.13%, and 0.43% as compared to the sub-optimal model in three test scenes, respectively. In addition, the effectiveness and superiority of the key components of S3T-Net are demonstrated from various experiments. As a reliable and competent emotion recognition model, the proposed S3T-Net contributes to the development of intelligent sentiment analysis in human–computer interaction (HCI) realm.

Implementation of Nonadiabatic Molecular Dynamics for Intersystem Crossing Based on a Time-Dependent Density-Functional Tight-Binding Method.

Intersystem crossing (ISC) and internal conversion (IC) are types of nonadiabatic transitions that play important roles in a wide range of fields, including photochemistry, photophysics, and photobiology. The nonadiabatic molecular dynamics (NA-MD) method is a powerful tool for computational simulations of dynamic phenomena involving nonadiabatic transitions. In this study, we implemented the NA-MD method, which treats ISC and IC on an equal footing, where the electronic structure is treated at the level of the time-dependent (TD) density-functional tight-binding (DFTB) method, a low-cost semiempirical analog of TD density functional theory (DFT). In particular, the spin-orbit coupling calculation algorithm was implemented in the TD-DFTB framework, and the results showed trends similar to those obtained using TD-DFT. In addition, the NA-MD method successfully reproduced ultrafast ISC of 2-nitronaphthalene.

Rat-Tail Models for Studying Hand-Arm Vibration Syndrome: A Comparison between Living and Cadaver Rat Tails

Over-exposure of the hand-arm system to intense vibration and force over time may cause degeneration of the vascular, neurological, and musculoskeletal systems in the fingers. A novel animal model using rat tails has been developed to understand the health effects on human fingers exposed to vibration and force when operating powered hand tools or workpieces. The biodynamic responses, such as vibration stress, strain, and power absorption density, of the rat tails can be used to help evaluate the health effects related to vibration and force and to establish a dose-effect relationship. While the biodynamic responses of cadaver rat tails have been investigated, the objective of the current study was to determine whether the biodynamic responses of living rat tails are different from those of cadaver rat tails, and whether the biodynamic responses of both living and cadaver tails change with exposure duration. To make direct comparisons, the responses of both cadaver and living rat tails were examined on four different testing stations. The transfer function of each tail under a given contact force (2 N) was measured at each frequency in the one-third octave bands from 20 to 1000 Hz, and used to calculate the mechanical system parameters of the tails. The transfer functions were also measured at different exposure durations to determine the time dependency of the response. Differences were observed in the vibration biodynamic responses between living and cadaver tails, but the general trends were similar. The biodynamic responses of both cadaver and living rat tails varied with exposure duration.

Hybrid mechanism of electrical breakdown in ferroelectric materials under high-pressure shock loading

The unique ability of ferroelectrics to generate high voltage under shock loading is limited by electrical breakdown within the shock-compressed ferroelectric material. Breakdown is a hybrid process of initiation and growth. The possible mechanisms of electrical breakdown in ferroelectric films and bulk ceramics subjected to high-pressure shock loading are discussed and experiments designed to elucidate which mechanisms govern breakdown. Gigapascal shock loading experiments were performed on poled Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3 ferroelectric film specimens in the range of 32–156 μm thickness to determine the dependence of the breakdown field on thickness and on film specimens in the range of 4–16 mm length to determine the dependence of the breakdown field on the duration of shock compression. The resulting breakdown-field vs thickness and breakdown-field vs shock transit time dependencies are consistent with a hybrid electron emission initiation and Joule heating microchannel growth mechanism. Further analysis of data previously obtained on shock-compressed 0.27Pb(In1/2Nb1/2)O3–0.47Pb(Mg1/3Nb2/3)O3–0.26PbTiO3 ferrvoelectric single crystals and Pb(Zr0.65Ti0.35)O3, Pb0.99(Zr0.52Ti0.48)0.99Nb0.01O3, Pb0.99(Zr0.95Ti0.05)0.98Nb0.02O3 bulk ceramics is consistent with this dual mechanism. It appears that neither chemical composition nor microstructure (single crystal vs polycrystalline) of the ferroelectric material has a significant effect on the breakdown mechanism in shocked ferroelectrics.

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time. Published by the American Physical Society 2024

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time. Published by the American Physical Society 2024

Polygenic hazard score models for the prediction of Alzheimer's free survival using the lasso for Cox's proportional hazards model.

The prediction of the susceptibility of an individual to a certain disease is an important and timely research area. An established technique is to estimate the risk of an individual with the help of an integrated risk model, that is, a polygenic risk score with added epidemiological covariates. However, integrated risk models do not capture any time dependence, and may provide a point estimate of the relative risk with respect to a reference population. The aim of this work is twofold. First, we explore and advocate the idea of predicting the time-dependent hazard and survival (defined as disease-free time) of an individual for the onset of a disease. This provides a practitioner with a much more differentiated view of absolute survival as a function of time. Second, to compute the time-dependent risk of an individual, we use published methodology to fit a Cox's proportional hazard model to data from a genetic SNP study of time to Alzheimer's disease (AD) onset, using the lasso to incorporate further epidemiological variables such as sex, APOE (apolipoprotein E, a genetic risk factor for AD) status, 10 leading principal components, and selected genomic loci. We apply the lasso for Cox's proportional hazards to a data set of 6792 AD patients (composed of 4102 cases and 2690 controls) and 87 covariates. We demonstrate that fitting a lasso model for Cox's proportional hazards allows one to obtain more accurate survival curves than with state-of-the-art (likelihood-based) methods. Moreover, the methodology allows one to obtain personalized survival curves for a patient, thus giving a much more differentiated view of the expected progression of a disease than the view offered by integrated risk models. The runtime to compute personalized survival curves is under a minute for the entire data set of AD patients, thus enabling it to handle datasets with 60,000-100,000 subjects in less than 1 h.

Time-dependent characteristics of analytical measurands.

Biological variation is a relevant component of diagnostic uncertainty. In addition to within-subject andbetween-subject variation, preanalytical variation also includes components that contribute to biological variability. Among these, daily recurring, i.e.,diurnal physiological variation is of particular importance, as it contains both a random and a non-random component ifthe exact time of blood collection is not known. We introduce four time-dependent characteristics (TDC) of diurnal variations for measurands to assess the relevance and extent of time dependence on the evaluation of laboratory results. TDC address (i)a threshold for considering diurnality, (ii) the expected relative changes per time unit, (iii) the permissible time interval between two blood collections at different daytimes within which the expected time dependence does not exceed a defined analytical uncertainty, and (iv) a rhythm-expanded reference change value. TDC and their importance will be exemplified by the measurands aspartate aminotransferase, creatine kinase, glucose, thyroid stimulating hormone, and total bilirubin. TDCs are calculated for four time slots that reflect known blood collection schedules, i.e.,07:00-09:00, 08:00-12:00, 06:00-18:00, and 00:00-24:00. The amplitude and the temporal location of the acrophase are major determinates impacting the diagnostic uncertainty and thus the medical interpretation, especially within the typical blood collection time from 07:00 to 09:00. We propose to check measurands for the existence of diurnal variations and, if applicable, to specify their time-dependent characteristics as outlined in our concept.

Effect and mechanism of time-dependent and economical expansion materials in improving the active roof-contact for cemented paste backfill

During the backfilling process, there is often a problem of no roof-contact, and the time and state of roof-contact cannot be predicted, seriously affecting the backfilling safety and efficiency. Therefore, the expansion effect, mechanism, and time dependence of the expansion agents used to achieve roof-contact were studied through expansion ratio tests, strength tests, and microscopic analysis. The expansion ratio of the MgO-type expansion agent (MEA) can meet the requirement of backfilling, and the unconfined compressive strength (UCS) of the expansive cemented paste backfill (ECPB) was attenuated compared to that of ordinary cemented paste backfill (CPB). Through scanning electron microscope (SEM) and mercury intrusion porosimetry (MIP) of the MgO-type ECPB, it is found that the ECB produces Mg(OH)2 crystals, which improves the compensation space inside the ECPB. MIP analysis results also show that the ECPB has higher porosity and more macropores, which is the reason for the strength attenuation of the ECPB. It is found that the expansion ratio and sedimentation ratio of fresh ECPB are time-dependent, and they both conform to logarithmic function. Afterwards, through the dynamic relationship between the sedimentation and expansion of fresh ECPB, the synthetic criterion of roof-contact based on the time-dependent model of expansion ratio and sedimentation ratio was established. The theoretical shortest roof-contact time of different experimental groups was obtained. Finally, through a comparative analysis of backfilling costs, the lowest cost and reasonable backfilling scheme were obtained. It is of great value for judging the effectiveness of roof contact, optimizing the backfilling proportion scheme, ensuring backfilling safety, and saving backfilling and mining costs.

Systematic experimental and model-based evaluation of the synergistic effects of alloy composition and damage rate on the formation of Cr-rich precipitates in Fe–Cr–Al alloys under ion irradiation

Fourteen Fe–Cr–Al alloys with systematically varied Cr and Al compositions were irradiated at 350∘C to 0.24 dpa by 10.5 MeV self-ions as model alloys for the Fe–Cr–Al (oxide dispersion strengthened: ODS) alloys being developed as accident tolerant fuel (ATF) cladding for light water reactors. Three dose rates (8×10−6, 8×10−5, and 8×10−4 dpa/s) were selected to predict the formation behavior of Cr-rich precipitates (CrRP) under neutron irradiation conditions. The effects of Cr, Al composition, and dose rate on the CrRP formation behavior were evaluated using a three-dimensional atom probe (3DAP) analysis. The results showed that the CrRP number density, volume fraction, and Cr concentration increase with increasing Cr composition, decreasing Al composition, and decreasing dose rate. Multiple regression analysis showed that in addition to these primary effects, there was an interaction between them on the CrRP volume fraction: (1) the higher the Al composition, the smaller the increase in the CrRP volume fraction with increasing Cr composition, and (2) the lower the Cr composition, the smaller the increase in the CrRP volume fraction with the decreasing Al composition and dose rate. It was also highlighted that to understand the dose rate effect on the CrRP formation behavior under neutron irradiation, it is useful to examine the irradiation time dependence, including the effective use of thermal aging data as a limit to the zero dose rate, in addition to the dose-dependency perspective. In addition to the systematic database of CrRP-related quantities established in this study, these considerations should contribute to further developing and validating numerical prediction models.