Proportionality Constant Research Articles

Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D

We investigate a new algebra-based approach of finding Grassmannian formulas for scattering amplitudes. Our prime motivation is massive amplitudes of 4D mathcal{N} = 4 SYM, and therefore we consider a 6D Grassmannian formula, where we can take advantage of massless kinematics. We next use symmetry arguments, and in particular, 6D dual conformal symmetry generalized to arbitrary dual conformal weights. Assuming a rational ansatz in terms of Plücker coordinates (i.e. minors) for the integrand, this approach leads to a set of algebraic equations. As an example, we explicitly find the solution for 4-point scattering amplitudes up to proportionality constants.

An Investigation of Grid Stability and a New Design of Adaptive Phase-Locked Loop for Wind-Integrated Weak Power Grid

This work investigates the impact of phase-locked loop (PLL) parameters on the stability of a wind-integrated weak power grid. The analysis is based on a weak grid model that integrates a Type-4 wind turbine generator with the grid represented by a lumped group model of a thermal power station with a steam governor and exciter system through a variable impedance network. This model is classically used for a weak grid study representing a real-life system. First, the impact of proportional and integral gain constants of the PLL on stability and oscillation characteristics is discussed in detail. Based on the analysis, an adaptive gain scheduling PI-based PLL architecture is proposed. The advantages of the proposed architecture are studied based on rigorous changes in the grid impedances and the wind dynamics. The results show that the proposed architecture significantly improves grid stability and damping when compared with conventional PLL designs.

Statistical Evaluation and Trend Analysis of ANN Based Satellite Products (PERSIANN) for the Kelani River Basin, Sri Lanka

Satellite-based precipitation products, (SbPPs) have piqued the interest of a number of researchers as a reliable replacement for observed rainfall data which often have limited time spans and missing days. The SbPPs possess certain uncertainties, thus, they cannot be directly used without comparing against observed rainfall data prior to use. The Kelani river basin is Sri Lanka’s fourth longest river and the main source of water for almost 5 million people. Therefore, this research study aims to identify the potential of using SbPPs as a different method to measure rain besides using a rain gauge. Furthermore, the aim of the work is to examine the trends in precipitation products in the Kelani river basin. Three SbPPs, precipitation estimation using remotely sensed information using artificial neural networks (PERSIANN), PERSIANN-cloud classification system (CCS), and PERSIANN-climate data record (CDR) and ground observed rain gauge daily rainfall data at nine locations were used for the analysis. Four continuous evaluation indices, namely, root mean square error (RMSE), (percent bias) PBias, correlation coefficient (CC), and Nash‒Sutcliffe efficiency (NSE) were used to determine the accuracy by comparing against observed rainfall data. Four categorical indices including probability of detection (POD), false alarm ratio (FAR), critical success index (CSI), and proportional constant (PC) were used to evaluate the rainfall detection capability of SbPPs. Mann‒Kendall test and Sen’s slope estimator were used to identifying whether a trend was present while the magnitudes of these were calculated by Sen’s slope. PERSIANN-CDR performed well by showing better performance in both POD and CSI. When compared to observed rainfall data, the PERSIANN product had the lowest RMSE value, while all products indicated underestimations. The CC and NSE of all three products with observed rainfall data were also low. Mixed results were obtained for the trend analysis as well. The overall results showed that all three products are not a better choice for the chosen study area.

Low ferrimagnetic damping in Gd3Fe5O12 epitaxial films grown using pulsed laser deposition

The magnetic damping constant is a proportionality constant for energy dissipation upon the precession of the magnetic moment, and it characterizes magnetization dynamics. In this study, ferrimagnetic Gd3Fe5O12 (111) epitaxial films are grown using pulsed laser deposition, and the temperature dependence of the ferrimagnetic resonance and damping constant (αFiM) is investigated. The results reveal that αFiM is approximately an order of magnitude smaller than those of other ferrimagnetic metals reported to date. Our results emphasize the potential of Gd3Fe5O12 films in ultralow-power spintronic applications.

Hybrid ensemble-variational data assimilation in ABC-DA within a tropical framework

Abstract. Hybrid ensemble-variational data assimilation (DA) methods have gained significant traction in recent years. These methods aim to alleviate the limitations and maximise the advantages offered by ensemble or variational methods. Most existing hybrid applications focus on the mid-latitudinal context; almost none have explored its benefits in the tropical context. In this article, hybrid ensemble-variational DA is introduced to a tropical configuration of a simplified non-hydrostatic convective-scale fluid dynamics model (the ABC model, named after its three key parameters: the pure gravity wave frequency A, the controller of the acoustic wave speed B, and the constant of proportionality between pressure and density perturbations C), and its existing variational framework, the ABC-DA system. The hybrid ensemble-variational DA algorithm is developed based on the alpha control variable approach, often used in numerical weather prediction. Aspects of the algorithm such as localisation (used to mitigate sampling error caused by finite ensemble sizes) and weighting parameters (used to weight the ensemble and climatological contributions to the background error covariance matrix) are implemented. To produce the flow-dependent error modes (ensemble perturbations) for the ensemble-variational DA algorithm, an ensemble system is also designed for the ABC model which is run alongside the hybrid DA system. A random field perturbations method is used to generate an initial ensemble which is then propagated using the ensemble bred vectors method. This setup allows the ensemble to be centred on the hybrid control analysis. Visualisation software has been developed to focus on the diagnosis of the ensemble system. To demonstrate the hybrid ensemble-variational DA in the ABC-DA system, sensitivity tests using observing system simulation experiments are conducted within a tropical framework. A 30-member ensemble was used to generate the error modes for the experiments. In general, the best performing configuration (with respect to the “truth”) for the hybrid ensemble-variational DA system used an 80%/20% weighting on the ensemble-derived/climatological background error covariance matrix contributions. For the horizontal wind variables though, full weight on the ensemble-derived background error covariance matrix (100%/0%) resulted in the smallest cycle-averaged analysis root mean square errors, mainly due to large errors in the meridional wind field when contributions from the climatological background error covariance matrix were involved, possibly related to a sub-optimal background error covariance model. The ensemble bred vectors method propagated a healthy-looking DA-centred ensemble without bimodalities or evidence of filter collapse. The ensemble was under-dispersive for some variables but for others, the ensemble spread approximately matched the corresponding root mean square errors. Reducing the number of ensemble members led to slightly larger errors across all variables due to the introduction of larger sampling errors into the system.

Surface layer response to heterogeneous tree canopy distributions: roughness regime regulates secondary flow polarity

Large-eddy simulation was used to model turbulent atmospheric surface layer (ASL) flow over canopies composed of streamwise-aligned rows of synthetic trees of height, $h$ , and systematically arranged to quantify the response to variable streamwise spacing, $\delta _1$ , and spanwise spacing, $\delta _2$ , between adjacent trees. The response to spanwise and streamwise heterogeneity has, indeed, been the topic of a sustained research effort: the former resulting in formation of Reynolds-averaged counter-rotating secondary cells, the latter associated with the $k$ - and $d$ -type response. No study has addressed the confluence of both, and results herein show secondary flow polarity reversal across ‘critical’ values of $\delta _1$ and $\delta _2$ . For $\delta _2/\delta \lesssim 1$ and $\gtrsim 2$ , where $\delta$ is the flow depth, the counter-rotating secondary cells are aligned such that upwelling and downwelling, respectively, occurs above the elements. The streamwise spacing $\delta _1$ regulates this transition, with secondary cell reversal occurring first for the largest $k$ -type cases, as elevated turbulence production within the canopy necessitates entrainment of fluid from aloft. The results are interpreted through the lens of a benchmark prognostic closure for effective aerodynamic roughness, $z_{0,{Eff.}} = \alpha \sigma _h$ , where $\alpha$ is a proportionality constant and $\sigma _h$ is height root mean square. We report $\alpha \approx 10^{-1}$ , the value reported over many decades for a broad range of rough surfaces, for $k$ -type cases at small $\delta _2$ , whereas the transition to $d$ -type arrangements necessitates larger $\delta _2$ . Though preliminary, results highlight the non-trivial response to variation of streamwise and spanwise spacing.

Vortex shedding frequency of a moving obstacle in a Bose–Einstein condensate

We experimentally investigate the periodic vortex shedding dynamics in a highly oblate Bose–Einstein condensate using a moving penetrable Gaussian obstacle. The shedding frequency f v is measured as a function of the obstacle velocity v and characterized by a linear relationship of f v = a(v − v c) with v c being the critical velocity. The proportionality constant a is linearly decreased with a decrease in the obstacle strength, whereas v c approaches the speed of sound. When the obstacle size increases, both a and v c are decreased. We discuss a possible association of a with the Strouhal number in the context of universal shedding dynamics of a superfluid. The critical vortex shedding is further investigated for an oscillating obstacle and found to be consistent with the measured f v. When the obstacle’s maximum velocity exceeds v c but its oscillation amplitude is not large enough to create a vortex dipole, we observe that vortices are generated in the low-density boundary region of the trapped condensate, which is attributed to the phonon emission from the oscillating obstacle.

Mechano-Chemical Properties of Electron Beam Irradiated Polyetheretherketone.

In this study, the mechano-chemical properties of aromatic polymer polyetheretherketone (PEEK) samples, irradiated by high energy electrons at 200 and 400 kGy doses, were investigated by Nanoindentation, Brillouin light scattering spectroscopy and Fourier-transform infrared spectroscopy (FTIR). Irradiating electrons penetrated down to a 5 mm depth inside the polymer, as shown numerically by the monte CArlo SImulation of electroN trajectory in sOlids (CASINO) method. The irradiation of PEEK samples at 200 kGy caused the enhancement of surface roughness by almost threefold. However, an increase in the irradiation dose to 400 kGy led to a decrease in the surface roughness of the sample. Most likely, this was due to the processes of erosion and melting of the sample surface induced by high dosage irradiation. It was found that electron irradiation led to a decrease of the elastic constant C11, as well as a slight decrease in the sample’s hardness, while the Young’s elastic modulus decrease was more noticeable. An intrinsic bulk property of PEEK is less radiation resistance than at its surface. The proportionality constant of Young’s modulus to indentation hardness for the pristine and irradiated samples were 0.039 and 0.038, respectively. In addition, a quasi-linear relationship between hardness and Young’s modulus was observed. The degradation of the polymer’s mechanical properties was attributed to electron irradiation-induced processes involving scission of macromolecular chains.

Radial viscous fingering induced by an infinitely fast chemical reaction

A numerical insight into the radial displacement of two viscously stable reactants undergoing an infinitely fast chemical reaction is obtained. This work broadens the numerical knowledge about the interaction between chemical reaction and hydrodynamic instability. A suitable transformation is utilised to deal with an infinite dimensionless parameter and reduce computational cost. Viscous fingering instability originates when the product has a different viscosity than the reactants. We calculate the onset time $t_{on}$ when the instability begins to appear for different reactants by varying the log mobility ratio $R_c$ and the Péclet number $Pe$ . Based on $t_{on}$ , we divide the time domain into stable and unstable zones with respect to instability. This helps to characterise reactants so as to have a flow with/without instability. For a fixed $Pe$ and $\vert R_c \vert$ , it is found that $t_{on}$ is early for $R_c > 0$ in contrast to the result for rectilinear displacement. This results in a wider stable zone for $R_c < 0$ . Interestingly, it is found that the stable zone can be made independent of $Pe$ by using a careful rescaling and we obtain the dependence of the onset time of instability on $R_c$ and $Pe$ as $t_{on} \propto (\vert R_c\vert Pe^{\beta _1}-\beta _2)^{\beta _3}$ where the constant of proportionality and $\beta _i$ , $i=1,2,3$ , depend upon the sign of $R_c$ . In the unstable zone, we find that the length of the fingers depends upon the sign of $R_c$ , which is not observed for any radial displacement of reactants undergoing a slow or moderately fast chemical reaction.

Linear Free Energy Relationships in Electrostatic Catalysis

The use of electric fields to modify chemical reactions is a promising, emerging technique in catalysis. However, there exist few guiding principles, and rational design requires assumptions about the transition state or explicit atomistic calculations. Here, we present a linear free energy relationship, familiar in other areas of physical organic chemistry, that microscopically relates field-induced changes in the activation energy to those in the reaction energy, connecting kinetic and thermodynamic behaviors. We verify our theory using first-principles electronic structure calculations of a symmetric S$_\mathrm{N}$2 reaction and the dehalogenation of an aryl halide on gold surfaces and observe hallmarks of linear free energy relationships, such as the shifting to early and late transition states. We also report and explain a counterintuitive case, where the constant of proportionality relating the activation and reaction energies is negative, such that stabilizing the product increases the activation energy, i.e., opposite of the Bell-Evans-Polanyi principle.

The ACVIM consensus statement definition of left ventricular enlargement in myxomatous mitral valve disease does not always represent left ventricular enlargement

ObjectiveTo determine how frequently the current criteria for left ventricular enlargement in dogs misclassify healthy dogs as having left ventricular enlargement; to examine the effect of breed on diastolic left ventricular normalized dimensions (LVIDDN); to propose appropriate scaling exponents and reference limits for dogs. AnimalsEchocardiographic data from 1,124 healthy adult dogs, including 454 dogs weighing <20 kg. MethodsWe calculated power regression parameters (allometric scaling), including exponents and proportionality constants, for various subsets of the dogs (all dogs, dogs < 20 kg, generic dogs, and individual breeds with >10 observations) and derived upper reference limits for LVIDDN. We determined the proportions of dogs that would be identified as having left ventricular enlargement with each regression model compared to previously published reference limits or guidelines. We then identified breeds failing to conform to generic dog models. ResultsThe American College of Veterinary Internal Medicine-recommended scaling exponent (0.294) and criterion for identifying left ventricular enlargement (1.7) identified >10% of apparently healthy dogs as having left ventricular enlargement, with specific breeds being misclassified up to 50% of the time. However, with a scaling exponent of 0.33, a constant of 1.7 represented a normal left ventricular size in 97.5% of healthy dogs in both generic and non-conforming breeds. ConclusionsLeft ventricular internal dimension in diastole normalized to bodyweight is breed-dependent. A constant of 1.7 with a scaling exponent of 0.294 does not always represent ventricular enlargement; a scaling exponent of 0.33, with breed-specific reference limits for breeds that fail to conform to allometric models of generic dogs, reduces the misclassification of healthy dogs as having left ventricular enlargement.

Full‐state discrete‐time model‐based stability analysis and parameter design of dual active bridge converter in energy storage system

The dual active bridge (DAB) converter plays a crucial role in energy storage system application of DC microgrid. In such a cascade system, maintaining its stability is imperative for reliable operation of the DAB converter under constant current, constant power, and constant voltage charging mode. Firstly, the accurate discrete-time models considering parasitic resistances are applied for three charging modes to reveal the system dynamic characteristics. The discrete-time small-signal models for different operation modes are developed further which gives guidance in the controller's parameters design. Secondly, the comprehensive and systematic analysis of all the possible unstable phenomena for three charging modes are conducted according to the discrete-time model. Finally, the underlying mechanisms are revealed by analyzing the relationships among the state variables, the Floquet multipliers, and system parameters. It is demonstrated that the inductor and output capacitor of the DAB converter, the DC bus voltage, the equivalent series resistance of the battery, and the proportional constant can influence the system stability under all charging modes greatly. Hence, the stability-oriented parameter design process is given which can provide the guidance in practical. The theoretical analysis under these three types operating modes is verified by simulations and experimental results.

Dark Energy Explained by a Bias in the Measurements

Typical cosmological models are based on the postulate that space is homogeneous. Space however contains overdense regions in which matter is concentrating, leaving underdense regions of almost void. The evolution of the scale factor of the universe has been established from measurements on SNIa. Since such events occur in regions were matter is present, we may expect that most of the SNIa are located in overdense regions. This means that the evolution of the scale factor has been established in a biased manner, by considering only information coming from overdense regions, excluding the one from the underdense regions. We develop a simple model to analyze the effect of this bias, and show that it leads to the appearance of a new tensor in the Einstein equation of general relativity, which can account for the apparent acceleration of the expansion of the universe. We further show that this tensor tends to be proportional to the FLRW metric tensor, and that the constant of proportionality quantitatively corresponds to the measured cosmological constant with a remarkable accuracy. We finally explain why these properties remain valid for other techniques used in determining the dynamics of the universe, such as the baryon acoustic oscillations.

Gravitational quasinormal modes for Lifshitz black branes

We study the scalar and vector channels of gravitational quasinormal modes for Lifshitz black branes emerging in Einstein-Maxwell-Dilaton and Einstein-Proca theories in four and five dimensions, finding significant differences between the two models. In particular, rather surprisingly, in the Einstein-Maxwell-Dilaton model the dispersion relations for the shear and sound modes are given by ωshear ∼ −i k4 and ωsound ∼ −i k2, while in the Einstein-Proca model they take the more conventional form ωshear ∼ −i k2 and ωsound ∼ k —the proportionality constants depend on the dynamical exponent and the appropriate factors of temperature. Through the holographic duality, this calculation provides information about the relaxation of the momentum and energy flux operators in a putative dual Lifshitz field theory. Comparing with the dispersion relations obtained directly by considering Lifshitz hydrodynamics suggest that the mass density of the equilibrium state in the Einstein-Maxwell-Dilaton model is infinite.

ELUCIDATING THE FRACTAL NATURE OF POWDER BED IN SELECTIVE LASER MELTING OF METALLIC COMPONENTS

In this work, the fractal nature of Selective Laser Melting (SLM) additive manufacturing process (AM) is elucidated. Fractal dimension and lacunarity of metallic powders are calculated from Scanning Electron Microscopy (SEM) images adapted from literature. The complexity and homogeneity of the textures of the powder beds are also studied through the comparison of fractal dimension and lacunarity. It is found that better densification results are obtained when the powder bed’s fractal dimension is closer to the golden mean number of 1.618. Furthermore, this finding is extended to expressions for predicting the component’s bulk density produced via SLM by setting the [Formula: see text] exponent equal to the golden mean value and finding the proportionality constant, [Formula: see text], using a nonlinear least squares method. The proposed approach works well since theoretical prediction and experimental data compare well with root-mean-square-error (RMSE) values that do not exceed [Formula: see text]. This work sheds new light on enhancing additive manufacturing technologies considering the fractal nature of SLM since its process mathematical models are constructed around Euclidian space-time with continuous smooth assumptions that should be adapted to include the fractal nature of the manufacturing process aiming to improve their precision. The underlying interweaving of SLM, as a fractal process, and the golden mean number is revealed.

Powder Reuse in Laser-Based Powder Bed Fusion of Ti6Al4V-Changes in Mechanical Properties during a Powder Top-Up Regime.

The properties of Extra Low Interstitials (ELI) Ti6Al4V components fabricated via the laser-based powder bed fusion (L-PBF) process are prone to variation, particularly throughout a powder reuse regime. Interstitial pick-up of interstitial elements within the build chamber during processing can occur, most notably, oxygen, nitrogen, and hydrogen, which can impair the mechanical properties of the built component. This study analyses ELI Ti6Al4V components manufactured by the L-PBF process when subjected to a nine-stage powder reuse sequence. Mechanical properties are reported via hardness measurement and tensile testing. Results showed that from 0.099 wt.% to 0.126 wt.% oxygen content, the mean hardness and tensile strength increased from 367.8 HV to 381.9 HV and from 947.6 Mpa to 1030.7 Mpa, respectively, whereas the ductility (area reduction) reduced from around 10% to 3%. Statistical analysis based on the empirical model from Tabor was performed to determine the strength–hardness relationship. Results revealed a significant direct relationship between tensile strength and Vickers hardness with a proportionality constant of 2.61 (R-square of 0.996 and p-value of 6.57 × 10−6).

Influence of curing temperature on the hydration and strength development of Class G Portland cement

A broad experimental program has been performed to characterize the hydration and strength development of a Class G oil well cement under various curing temperatures from 15 to 87 °C. The progress of hydration was monitored by isothermal calorimetry, thermo-gravimetric analysis, and quantitative X-ray diffraction based on Rietveld refinement; while the strength development was evaluated by both nondestructive ultrasonic tests and destructive crush tests. Test results indicate that heat of hydration, non-evaporable water content and degree of hydration of the cement follow approximately linear relationships, which are largely independent of curing temperature; the obtained proportionality constants agree well with those estimated by previously proposed empirical equations. The influences of curing temperature on the hydration rate and strength development rate can be modeled by an equivalent age method coupled with the Arrhenius law. The apparent activation energy obtained from hydration analysis was higher than that obtained from strength development analysis.

A study on the isolated photon production in nuclear collisions at the CERN-LHC energies

An analysis of prompt photon production in high energy nuclear collisions at the Large Hadron Collider is performed within the parton saturation picture taking into account the updated phenomenological color dipole models. Comparison between ⟨N coll⟩ scaling for hard scattering in heavy-ion collisions and the N part-scaling based on geometric scaling arguments has been done. The predictions are parameter free in the first case whereas a dependence on the constant of proportionality κ between the number of participants and the nuclear saturation scale appears in the second case. This parameter has been analyzed in the prompt photon spectrum at small transverse momentum even though no fitting procedure was performed. Results are confronted with the measurements made by the ALICE, ATLAS, and CMS experiments in terms of photon transverse momentum at different rapidity bins. We show that the prompt photon production exhibits distinct scalings in AA events associated to geometrical properties of the collision and can be properly addressed in the color dipole formalism. Based on the N part-scaling, an analytical parametrization for the invariant cross section is provided and employed to predict the x T-scaling in measurements. For κ of order of unit the theoretical scaling curve correctly describes data in the range x T ⩽ 5 × 10−2.

Experimental study of temperature change effect on distributed acoustic sensing continuous measurements

Distributed fiber-optic sensing is useful in geophysical exploration and monitoring applications. Distributed temperature sensing (DTS) is used for measuring and monitoring temperature and distributed acoustic sensing (DAS) for recording the seismic wavefield. However, DAS measurements also are sensitive to temperature changes. To understand and quantify the DAS signature of temperature changes during water injections at CO2CRC Otway site, a series of experiments have been conducted at the Curtin University/National Geosequestration Laboratory (NGL) well research facility and Curtin rock-physics laboratory. Overall, three DAS cables are examined. Two fibers are tested in the laboratory and one cable, which is installed behind the casing in the Curtin/NGL well, is examined in the well. Laboratory measurements and observations made during analysis of passive DAS and DTS field data recorded in four Otway wells demonstrate that DAS is sensitive to long-period temperature changes, and its response is proportional to the time derivative of temperature. Induced fiber strain is linearly related to slow temperature change, and this dependency can be estimated for a particular cable. Obtained proportionality constants between strain and temperature change indicate some dependency on the cable type/design and acquisition setup, but they are all of the same order of magnitude. DAS measurements also can be affected by low-frequency noise possibly associated with the effect of temperature on the DAS acquisition unit itself. The results can help compensate for the effect of temperature on low-frequency DAS signals and show that DAS can be used as a distributed temperature sensor if direct temperature measurements are not available.

Characterization of \u03b3-H2AX foci formation under alpha particle and X-ray exposures for dose estimation

DNA double-strand break (DSB) induction is one of the phenotypes of cellular damage from radiation exposure and is commonly quantified by γ-H2AX assay with the number of excess fluorescent foci per cell as the main component. However, the number of foci alone may not fully characterize the state of DNA damage following exposures to different radiation qualities. This study investigated the feasibility of utilizing the focus size distribution and dephosphorylation rate of γ-H2AX to identify the type of causative radiation and dose. Human lung epithelial cells and mouse vascular endothelial cells were used to observe the expression changes of γ-H2AX foci due to alpha particle and X-ray exposures. Results showed that the average number of excess foci per cell linearly increased with the dose. The focus size distribution showed a consistent pattern depending on the causative radiation type. Three criteria for the identification of causative radiation type were derived from experimental focus size distributions and were validated in blind testing with correct identification of 27 out of 32 samples. The dose could be estimated based on the proportionality constant specific to the identified radiation type with a difference of less than 15% from the actual value. The different dephosphorylation rates of γ-H2AX produced from alpha particle and X-ray exposures were effectively utilized to determine the individual dose contributions of alpha particles and X-rays under mixed beam exposure. Individual doses were estimated to have differences of less than ~ 12% from actual values.