Correct Scaling Research Articles

Bose-Einstein condensation in Hořava-Lifshitz theory

In this paper we study the corrections emergent from a Hořava-Lifshitz extension of the complex scalar sector to the Bose-Einstein condensation and to the thermodynamics parameters. We initially discussed some features of the model to only then compute the corrections to the Bose-Einstein condensation. The calculations were done by computing the generating functional, from which we extract the thermodynamics parameters. We also obtained the Lifshitz scaling correction for the critical temperature T c that sets the Bose-Einstein condensation.

Boundary Critical Behavior of the Three-Dimensional Heisenberg Universality Class.

We study the boundary critical behavior of the three-dimensional Heisenberg universality class, in the presence of a bidimensional surface. By means of high-precision MonteCarlo simulations of an improved lattice model, where leading bulk scaling corrections are suppressed, we prove the existence of a special phase transition, with unusual exponents, and of an extraordinary phase with logarithmically decaying correlations. These findings contrast with naïve arguments on the bulk-surface phase diagram, and allow us to explain some recent puzzling results on the boundary critical behavior of quantum spin models.

Hardware in the loop experiments with ship propulsion systems in the towing tank: Scale effects, corrections and demonstration

Standards for environmental impact, safety and operational performance of ships are becoming increasingly strict. In order to meet these standards, the performance of new ship designs must be predicted with an increasing level of detail and confidence. As present prediction methods lack realistic, dynamic behaviour of the ship's propulsion plant, there is a need for more advanced methods. In this paper, an open water test with Hardware in the Loop (HIL) functionality is proposed. HIL open water tests combine software and hardware components to emulate realistic behaviour of the ship's propulsion plant in the towing tank. It is known, however, that experiments in the towing tank are subject to viscous scale effects. In addition to this, shaft dynamics are distorted by a number of scale effects occurring inside the scale model propulsion system. In this paper, it is demonstrated with measurements that if corrections for these scale effects are applied, the dynamic interaction between the propeller and simulated engine system can be accurately emulated in the ship model basin.

A nonlinear partially-averaged Navier–Stokes model with near-wall correction for separated turbulent flow

A nonlinear Partially-Averaged Navier–Stokes model with near-wall correction is developed for separated turbulent flow simulations. The periodic hills flow is simulated to validate the new model and the results are compared with the standard [Formula: see text] model, MPANS model, MSST PNAS model, standard [Formula: see text] PANS model, and experimental/LES results. It is found that the new model shows better performance in the prediction of both mean velocity and turbulent statistics compared to the other models. From the prediction of the near-wall friction coefficient of periodic hills flow, the new model shows good resolution in the near-wall region by considering the near-wall damping function to turbulent viscosity, gradient production term, and turbulence scale correction term for the near-wall region. From the analysis of anisotropy-invariant and sub-filtered stress (SFS), it can be found that the nonlinear term is necessary for prediction accuracy improvement in turbulent flow simulation with strong separation.

Compensating Local Magnifications in Atom Probe Tomography for Accurate Analysis of Nano-Sized Precipitates.

Local magnification artifacts in atom probe tomography (APT) caused by multiphase materials with heterogeneous evaporation behavior are a well-known problem. In particular, the analysis of the exact size, shape, and composition of small precipitates is, therefore, not trivial. We performed numerical simulations of APT measurements to predict the reconstructed morphology of precipitates with contrasting evaporation thresholds. Based on a statistical approach that avoids coarse graining, the simulated data are evaluated to develop a model for the calculation of the original size of the precipitates. The model is tested on experimental APT data of precipitates with a higher and lower evaporation field in a ferritic alloy. Accurate sizes, proven by a complementary investigation by transmission electron microscopy, are obtained. We show further, how the size information can be used to obtain compositional information of the smallest precipitates and present a new methodology to determine a correct in-depth scaling of the APT reconstruction in case no complementary geometric information about the specimen exists or if no lattice planes are visible in the reconstruction.

On the zero point constant of the bolometric correction scale

ABSTRACT Arbitrariness attributed to the zero-point constant of the V-band bolometric corrections (BCV) and its relation to ‘bolometric magnitude of a star ought to be brighter than its visual magnitude’ and ‘bolometric corrections must always be negative’ was investigated. The falsehood of the second assertion became noticeable to us after IAU 2015 General Assembly Resolution B2, where the zero-point constant of bolometric magnitude scale was decided to have a definite value CBol(W) = 71.197 425 ... . Since the zero-point constant of the BCV scale could be written as C2 = CBol − CV, where CV is the zero-point constant of the visual magnitudes in the basic definition BCV = MBol − MV = mbol − mV, and CBol > CV, the zero-point constant (C2) of the BCV scale cannot be arbitrary anymore; rather, it must be a definite positive number obtained from the two definite positive numbers. The two conditions C2 > 0 and 0 < BCV < C2 are also sufficient for LV < L, a similar case to negative BCV numbers, which means that ‘bolometric corrections are not always negative’. In sum it becomes apparent that the first assertion is misleading causing one to understand bolometric corrections must always be negative, which is not necessarily true.

Spectrum calibration of the first hyperspectral infrared measurements from a geostationary platform: Method and preliminary assessment

AbstractThe level‐1 (L1) radiance spectra from the first Geostationary Interferometric InfraRed Sounder (GIIRS) have been publicly available since January 2019. On account of the inherent observation characteristics, operation modes, and capabilities, a complete spectrum calibration method of GIIRS/L1 products is originally proposed to form the latest version (V3) algorithm for implementation. Particularly, four targeted improvements in three aspects are independently established: subsample location alignment to yield integrated interferograms in both forward and backward directions with almost zero phase, rough spectral scale unification as well as accurate spectral scale correction to resolve spectral non‐uniformity due to a seriously asymmetric configuration of focal plane array, and an additional double‐reflected compensation to mitigate the influence of non‐ideal onboard blackbody reference upon radiometric accuracy. Preliminary assessments from both domestic and international sources indicate that the spectral and radiometric accuracies of the measured spectra from the latest GIIRS/L1 V3 algorithm show a well‐behaved performance in both longwave (LW) and midwave (MW) bands, that is, lower than 10 ppm of spectral scale errors, which is of sufficient accuracy for numerical weather prediction use, and around 1 K for most uncontaminated channels within the LW band. However, non‐linearity correction of interferograms and spectral quality improvements, especially for the MW band, should be developed further. In general, a feasible solution of spectrum calibration for a hyperspectral sounder on geostationary platform is provided in detail for reference, which is expected to benefit users of GIIRS data as well as designers responsible for L1 data processing of other similar sensors.

Second time scale of the metastability of reversible inclusion processes

We investigate the second time scale of the metastable behavior of the reversible inclusion process in an extension of the study by Bianchi et al. (Electron J Probab 22:1–34, 2017), which presented the first time scale of the same model and conjectured the scheme of multiple time scales. We show that $$N/d_{N}^{2}$$ is indeed the correct second time scale for the most general class of reversible inclusion processes, and thus prove the first conjecture of the foresaid study. Here, N denotes the number of particles, and $$d_{N}$$ denotes the small scale of randomness of the system. The main obstacles of this research arise in calculating the sharp asymptotics for the capacities, and in the fact that the methods employed in the former study are not directly applicable due to the complex geometry of particle configurations. To overcome these problems, we first thoroughly examine the landscape of the transition rates to obtain a proper test function of the equilibrium potential, which provides the upper bound for the capacities. Then, we modify the induced test flow and precisely estimate the equilibrium potential near the metastable valleys to obtain the correct lower bound for the capacities.

Stable charged radiating systems associated with tilted observers

This paper is aimed to study the influence of electromagnetic field and tilted congruences on the dynamical features of self-gravitating system. We shall explore the stability of homogeneous energy density in the background of Maxwell-Palatini $f(R)$ gravity. In this respect, we have considered an irrotational non-static planar geometry which is assumed to have two different types of gravitating sources. The role of tilted congruences and the geodesic motion of an evolving system is studied through the divergence of the entropy vector field. The condition for the emergence of Minskoskian cavity is also explored. In order to connect tilted and non-tilted reference frames with inflationary and inverse Ricci scalar corrections in the charged medium, few well-consistent relations are presented. It is concluded that effective electric charge is trying to increase the stability of regular energy density of the planar system.

Reaction rates and the noisy saddle-node bifurcation: Renormalization group for barrier crossing

Barrier crossing calculations in chemical reaction-rate theory typically assume that the barrier is large compared to the temperature. When the barrier vanishes, however, there is a qualitative change in behavior. Instead of crossing a barrier, particles slide down a sloping potential. We formulate a renormalization group description of this noisy saddle-node transition. We derive the universal scaling behavior and corrections to scaling for the mean escape time in overdamped systems with arbitrary barrier height. We also develop an accurate approximation to the full distribution of barrier escape times by approximating the eigenvalues of the Fokker-Plank operator as equally spaced. This lets us derive a family of distributions that captures the barrier crossing times for arbitrary barrier height. Our critical theory draws links between barrier crossing in chemistry, the renormalization group, and bifurcation theory.

On the logic of collapsibility for causal effect measures.

On the logic of collapsibility for causal effect measures.

Absolute Calibration of Diffuse Radio Surveys at 45 and 150 MHz

Abstract We use measurements from the Experiment to Detect the Global EoR Signature (EDGES) to determine scale and zero-level corrections to the diffuse radio surveys by Guzmán et al. at 45 MHz and by Landecker & Wielebinski at 150 MHz. We find that the map of Guzmán et al. requires a scale correction of 1.076 ± 0.034 (2σ) and a zero-level correction of −160 ± 78 K (2σ) to best-fit the EDGES data. For the map of Landecker & Wielebinski, the scale correction is 1.112 ± 0.023 (2σ) and the zero-level correction is 0.7 ± 6.0 K (2σ). The correction uncertainties are dominated by systematic effects, of which the most significant are uncertainty in the calibration of the EDGES receivers, antenna pointing, and tropospheric and ionospheric effects. We propagate the correction uncertainties to estimate the uncertainties in the corrected maps themselves and find that the 2σ uncertainty in the map brightness temperature is in the range 3.2%–7.5% for the map of Guzmán et al. and 2.1%–9.0% for the map of Landecker & Wielebinski, with the largest percentage uncertainties occurring at high Galactic latitudes. The corrected maps could be used to improve existing diffuse low-frequency radio sky models, which are essential tools in analyses of cosmological 21 cm observations, as well as to investigate the existence of a radio monopole excess above the cosmic microwave background and known Galactic and extragalactic contributions.

A Vector Ionospheric Delay Correction Method for GNSS Positioning and Navigation Wide Area Augmentation Service

A new ionospheric delay correction method is proposed to improve the ionospheric correction accuracy of single frequency GNSS users. In the new method, the ionospheric grid point information is expanded from a single scalar vertical correction parameter to a vector of triple elements (the triple): vertical correction parameter, north correction parameter and east correction parameter. The new parameters are used to describe the variation of ionospheric delay correction caused by satellite azimuth. Using the observation data of the ground monitoring stations to fit the triple, and then broadcast the triple to the user. GNSS single frequency users can use the triple data to correct their own ionospheric delay. The testing results show that the correction error of the method is around 0.3 m lower than that of the scalar method.

Describing polymer polarizability with localized orbital scaling correction in density functional theory.

Polarizability reflects the response of the molecular charge distribution to an applied external electric field and thus closely relates to the molecular electron density. For the calculation of polarizability within density functional theory (DFT), it is well known that conventional density functional approximations (DFAs) greatly overestimate the results for polymers with long chains and the π-conjugated system. This is a manifestation of the delocalization error of the commonly used DFAs-they normally produce too delocalized electron density and underestimate the total energy for systems with fractional charge character, which occurs for long molecules in a longitudinal electric field. Thus, to achieve an accurate description of polarizabilities for polymeric molecular systems from DFT, applying DFAs with minimal delocalization error is very important. In this work, we use the recently developed localized orbital scaling correction (LOSC) to the conventional DFAs, which has been shown to largely eliminate the delocalization error, to calculate and study the polarizabilities of three classic polymers, polyyne, polyacetylene, and hydrogen chain. The results from this work demonstrate that applying LOSC to conventional DFAs with self-consistent field calculations can largely improve the description of polarizability from DFT calculations and the improved quality of electron density in LOSC leads to the improved results of polarizability of the polymers. However, the improvement is not complete and adjustment of the parameters in the LOSC method can further improve the accuracy to reach the level similar to the MP2 method. This work also points to the direction for the further development of LOSC in self-consistent calculations.

Displacement autocorrelation functions for strong anomalous diffusion: A scaling form, universal behavior, and corrections to scaling

Strong anomalous diffusion is characterized by asymptotic power-law growth of the moments of displacement, with exponents that do not depend linearly on the order of the moment. The exponents concerning small-order moments are dominated by random motion, while higher-order exponents grow by faster trajectories, such as ballistic excursions or "light fronts". Often such a situation is characterized by two linear dependencies of the exponents on their order. Here, we introduce a simple exactly solvable model, the Fly-and-Die (FnD) model, that sheds light on this behavior and on the consequences of light fronts on displacement autocorrelation functions in transport processes. We present analytical expressions for the moments and derive a scaling form that expresses the long-time asymptotics of the autocorrelation function $\langle x(t_1)\,x(t_2)\rangle$ in terms of the dimensionless time difference $(t_2-t_1)/t_1$. The scaling form provides a faithful collapse of numerical data for vastly different systems. This is demonstrated here for the Lorentz gas with infinite horizon, polygonal billiards with finite and infinite horizon, the L\'evy-Lorentz gas, the Slicer Map, and L\'evy walks. Our analysis also captures the system-specific corrections to scaling.

Smart Artificial Markers for Accurate Visual Mapping and Localization.

Artificial marker mapping is a useful tool for fast camera localization estimation with a certain degree of accuracy in large indoor and outdoor environments. Nonetheless, the level of accuracy can still be enhanced to allow the creation of applications such as the new Visual Odometry and SLAM datasets, low-cost systems for robot detection and tracking, and pose estimation. In this work, we propose to improve the accuracy of map construction using artificial markers (mapping method) and camera localization within this map (localization method) by introducing a new type of artificial marker that we call the smart marker. A smart marker consists of a square fiducial planar marker and a pose measurement system (PMS) unit. With a set of smart markers distributed throughout the environment, the proposed mapping method estimates the markers’ poses from a set of calibrated images and orientation/distance measurements gathered from the PMS unit. After this, the proposed localization method can localize a monocular camera with the correct scale, directly benefiting from the improved accuracy of the mapping method. We conducted several experiments to evaluate the accuracy of the proposed methods. The results show that our approach decreases the Relative Positioning Error (RPE) by 85% in the mapping stage and Absolute Trajectory Error (ATE) by 50% for the camera localization stage in comparison with the state-of-the-art methods present in the literature.

Impact of explicit area scaling on kinetic models involving multiple compartments

BackgroundComputational modelling of cell biological processes is a frequently used technique to analyse the underlying mechanisms and to generally understand the behaviour of these processes in the context of a pathway, network or even the whole cell. The most common technique in this context is the usage of ordinary differential equations that describe the kinetics of the relevant processes in mechanistic detail. Here, it is usually assumed that the content of the cell is well-stirred and thus homogeneous - which is of course an over-simplification, but often worked in the past. However, many processes happen at membranes and thus not in 3D, but in 2D. The scaling of the rates of these processes poses a special problem, if volumes of compartments are changed. They will typically scale with an area, but not with the volume of the involved compartment. However, commonly, this is neglected when setting up models and/or volume scaling also sometimes automatically happens when using modelling software in the field.ResultsHere, we investigate generic as well as specific, realistic cases to find out, how strong the impact of the wrong scaling is for the outcome of simulations. We show that the importance of correct area scaling depends on the architecture of the reaction site and its changes upon volume alterations and it is hard to foresee, if it has a significant impact or not just by looking at the original model set-up. Moreover, scaled rates might exhibit more or less control over the behaviour of the system and therefore, accordingly, incorrect scaling will have more or less influence.ConclusionsWorking with multi-compartment reactions requires a careful consideration of the correct scaling of the rates when changing the volumes of the involved compartments. The error following incorrect scaling - often done by scaling with the volume of the respective compartments can lead to significant aberrations of model behaviour.

3D plant root system reconstruction based on fusion of deep structure-from-motion and IMU

Roots play a critical role in the functioning of plants. However, it is still challenging to generate detailed 3D models of thin and complicated plant roots, due to the complexity of the structure and the limited textures. Limited by the difficulty of realization and inaccessibility of labeled data for training, few works have been put in exploring this problem using deep neural networks. To overcome this limitation, this paper presents a structure-from-motion based deep neural network structure for plant root reconstruction in a self-supervised manner, which can be applied by mobile phone platforms. In the training process of deep structure-from-motion, each depth is constrained from the depth map and predicted relative poses from their adjacent frames captured by the mobile phone cameras, and the LSTM-based network after CNN for pose estimation is learnt from the ego-motion constraints by further exploiting the temporal relationship between consecutive frames. IMU unit in the mobile phone is further utilized to improve the pose estimation network by continuously updating the correct scales from the gyroscope and accelerometer moment. Our proposed approach is able to solve the scale ambiguity in recovering the absolute scale of the real plant roots so that the approach can promote the performance of camera pose estimation and scene reconstruction jointly. The experimental results on both real plant root dataset and the rendered synthetic root dataset demonstrate the superior performance of our method compared with the classical and state-of-the-art learning-based structure-from-motion methods.

Відображення R-оцінок рівня фінансового стану підприємства на вербально-числовій шкалі

The publication considers the features of construction of the so-called «Harrington’s scale», which is widely used for economic research in Ukraine. It is demonstrated that the scale proposed by Harrington cannot be applied for arbitrary economic indicators. For the purposes of this study, an analysis of the applicability of the Harrington’s function for specific economic studies is carried out and it is shown that the «Harrington’s scale» cannot be applied to economic indicators, the increase in the value of which indicates an increase in the «quality» of the functioning of enterprise, for example, such as the «economic potential of the enterprise» or the enterprise’s «level of financial condition» (the latter requires the construction of a verbal scale according to the new probabilistic principle which is considered in this article). The indicator of «level of financial condition» is chosen because, as a rule, the current monitoring of the financial condition of enterprise is to be carried out automatically, by means of the appropriate tools, based on the multi-criteria methods for assessing the level of financial condition. One of these methods is the method of R-assessment of the financial condition of enterprise according to the Sayfullin – Kadykov model, which takes into account five criteria and puts them in line with the R-assessment. The article considers the main provisions of Harrington’s work in order to provide the possibility of correct use of the Harrington’s desirability function for the qualitative assessment of economic indicators, including complex and integral indicators that are used to monitor the financial condition of enterprise. The article proposes another function in place of desirability function, namely the function of distribution of the indicator under research, whether theoretical or empirical. In addition, the limit values that separate the different values of the linguistic variable at the base interval are proposed to be determined according to the statistics of the group of companies to which the enterprise under research belongs, or can be included according to the criterion of homogeneity with any enterprise of the researched group. An example of constructing the correct qualitative scale for a normally distributed variable of «level of financial condition of the enterprise» at the probabilistic level is provided. Attention is drawn to the fact that the boundary values of the qualitative scale significantly depend on the law of distribution of the variable under research.

An improved scheme for image scaling, cropping and colour correction in encrypted domain

An improved scheme for image scaling, cropping and colour correction in encrypted domain