Shape Of Curve Research Articles

Hyper-viscoelastic characterization of the urethra

Abstract Hyper-viscoelastic models have been used to characterize large strains coupled with viscosity. In this study, we aimed to model the urethral in-vivo biomechanics through a hyper-viscoelastic implementation. First, we used isotropic 2-parameter Demiray model for identification of urethral tube inflation after refining the values of quasistatic states. Attempting the approach by Holzapfel et. al., the average ratio of the elastic and dynamic modulus was computed to determine the stress contribution of the viscoelastic branches. The values of the parameters were determined after constraining a constant Energy dissipation (generalized maxwell) over range 1s to 100s. For the hyper-viscoelastic comparison implementation, it was observed that the goodness of fit criteria performs good for half of the samples (Adjusted R2>0.95). In some samples, the model is limited to fit ‘S’ shape curves but still performed well. The above identification technique and the hyper-viscoelastic in-silico approaches show that our approach fares sufficiently for the creep response characterization of the urethra.

Research on resistivity characteristics of grain-coating and pore-filling hydrates in different sediment packings based on voxelated 3D models

Natural gas hydrate is a clean energy resource with abundant reserves. Before conducting large-scale exploitation, understanding its physical properties, such as electrical properties, is crucial for gas reserve evaluation and production process monitoring. Due to the complexity of the pore space geometry and different hydrate growth morphology, electrical resistivity may vary for different samples at the same hydrate saturation. This study considered three packings of unconsolidated marine sediment grains (simple cubic, body-centered cubic, and face-centered cubic) and two end distribution patterns of hydrates in pores (grain-coating and pore-filling). The original 3D geometries of hydrate-bearing models were replaced with voxelated meshes to achieve better stability and versatility. The resistivities of models were calculated using the finite element method and compared with the results from Archie's law. The simulation results show that the resistivity curve's shape is jointly affected by the hydrate distribution pattern and the initial pore space geometry. A rational function can be used to fit the saturation exponent curves to give critical brine saturations. The grain-coating hydrate prefers blocking the throats and has a critical brine saturation above 0. In contrast, the pore-filling hydrate has resistivities lower than the Maxwell-Garnett equation's lower boundary due to a bypassing effect, which partially compensates for the conductivity loss of the pore fluid and is more remarkable for models distributed by bigger hydrate particles, and has a critical brine saturation equal to 0. The findings are helpful in understanding the non-Archie phenomenon of hydrate-bearing sediments.

Agricultural economic complexity and regional inequalities: a new approach using census data from Brazil

ABSTRACT The paper presents an original application of economic complexity to the agricultural sector aiming to determine its suitability to measure and depict regional structural inequalities across Brazilian regions. Using census data, we calculate agricultural complexity indexes for products (PCI-Agro) and regions (ECI-Agro) and the agricultural product space. We show that higher PCI-Agro is associated with higher levels of productivity, education, income and human development. Also, we found that ECI-Agro is associated with higher productivity in agriculture. The econometric evidence points to an inverted ‘U’-shape curve relationship between ECI-Agro and agricultural productivity, which has significant policy implications.

Numerical analysis and runner shape optimization of a high head pump-turbine

Abstract A set of numerical approaches ranging from the time-consuming unsteady full turbine RANS approach to a very fast periodic steady-stage approach were considered for CFD simulation of flow in Francis pump-turbines. Their computational efforts and accuracy of efficiency prediction were assessed through comparison with experimental data in both pump and turbine modes. It was shown that the unsteady full turbine approach is needed for accurate simulation of low discharge regimes in pump mode. From the other hand, near the optimum and in the high discharge zone, periodic steady-stage approach can be utilized. Next, an approach for multi-objective runner shape optimization of pump-turbine runners was proposed. Thirty free design parameters allowed flexible variation of runner blade shape, hub and band curves, as well as the height of the distributor, linked to the guide vane opening angle. Two or three reference operating points, indicating the turbine performance and head in both turbine and pump modes, were taken for optimization. Cavitation characteristics were accounted for through special constraints. The approach was tested for a 500 m head pump-turbine. It was shown that the optimized runners significantly outperform the initial one in terms of efficiency with comparable cavitation performance.

A.S.S.E.S.S. for Facial Fillers.

An in-depth and detailed facial assessment is critical in treating and achieving desirable dermal filler and neurotoxin results. An acronym called A.S.S.E.S.S. simplifies an often complex and overwhelming amount of data needed to assimilate when performing facial filler and neurotoxin injections. Applying this method to patients in six simple steps provides a starting point and offers a guideline to capture key details for a more comprehensive facial assessment. The A.S.S.E.S.S. acronym stands for animate, shape, side, external, symmetry, and shadows and is helpful in following a methodical approach in analyzing facial shape, profile, and natural facial curves in both static and dynamic states. Following a regimented A.S.S.E.S.S. approach prior to treating filler and neurotoxin patients allows providers a straightforward guide to achieve a desirable facial shape and profile. This stepwise facial assessment establishes a logical and detailed approach to ensure the important aspects of facial details are appreciated in creating reliable and pleasing filler and neurotoxin results.

Association of dynamic changes in arterial partial pressure of carbon dioxide with neurological outcomes in aneurysmal subarachnoid hemorrhage

BackgroundCerebral blood flow (CBF) is closely regulated by carbon dioxide (CO2). In patients with aneurysmal subarachnoid hemorrhage (aSAH), abnormal arterial partial pressure of CO2 (PaCO2) might deteriorate brain injuries. Nevertheless, the impact of dynamic PaCO2 fluctuations on neurological outcomes in aSAH patients has not been extensively studied. Our study aimed to investigate the association between dynamic PaCO2 levels and unfavorable neurological outcomes in aSAH patients. MethodsIn this retrospective observational study, we consecutively enrolled 159 aSAH patients from December 2019 to July 2021. Arterial blood gas measurements within 10 days after intensive care unit (ICU) admission for each patient were recorded to calculate the time-weighted average (TWA)-PaCO2, an indicator representing the dynamic changes in PaCO2 levels. For the association between TWA-PaCO2 levels and unfavorable neurological outcomes in aSAH patients, multivariable logistic analysis was used to explore TWA-PaCO2 levels as categorical variables, and restricted cubic spline (RCS) was used to explore TWA-PaCO2 levels as continuous variables. ResultsIn multivariable logistic analysis, after adjusting confounders, when TWA-PaCO2 35–45 mmHg was as a reference, TWA-PaCO2 < 35 mmHg (odds ratio [OR] 2.15, 95 % confidence interval [CI] 0.83–5.55, P = 0.113) and TWA-PaCO2 > 45 mmHg (OR 8.31, 95 % CI 0.72–96.14, P = 0.090) were not independently associated with unfavorable neurological outcomes (modified Rankin score of 3–6). The RCS shows a “U” shape curve between TWA-PaCO2 levels and unfavorable neurological outcomes, with a nonlinear P-value of 0.023. The lowest ORs of unfavorable neurological outcomes were within PaCO2 32.8–38.1 mmHg. ConclusionsBoth lower and higher PaCO2 levels are harmful to aSAH patients. PaCO2 in the range of 32.8–38.1 mmHg is associated with lowest unfavorable neurological outcomes.

Enhancing data-driven-based state of health estimation for diverse battery applications through effective feature construction

Data-driven-based State of Health (SOH) estimation methods are popular for their ability to avoid considering the battery's complex aging mechanisms. However, aging features extracted from specific voltage intervals and the SOH estimation models established under specific conditions may no longer be applicable to other battery applications. This work first reveals the necessary conditions for constructing effective aging features in a partial voltage interval, and specifically proposes an applicable method for determining the voltage interval of constructing aging features based on the incremental capacity curve and the voltage curve's shape. The proposed method can be adapted to different battery applications and is suitable for partial charging conditions. Given the different aging patterns present in different battery types and applications, a feature self-scaling -based online learning strategy is developed to reduce the model's reliance on aging datasets and enable it to adapt to real-time battery aging patterns. The proposed methods are validated through both an actual aging experiment and three publicly available aging datasets, showcasing their effectiveness in extending the applicability of the proposed SOH estimation methods for diverse battery applications.

Study of the interference fringes-caustic region interaction in a topological Young's interferometer.

Herein, an analysis of the optical field emerging from a topological Young's interferometer is conducted. The interferometer consists of two 3D-slit shape curves and is studied by projecting it onto a trihedral reference system. From the projection, Airy, Pearcey, and cusped-type beams emerge. The optical field of these beams is organized around its caustic region. The interference between these types of beams presents interesting physical properties, which can be derived from the interaction between the interference fringes and the caustic regions. One property of the interaction is the irradiance flow, which induces a long-distance interaction between the caustic regions. Another property is the bending of the interference fringes toward the caustic regions, which acts as a sink. Due to the adiabatic features of the caustic regions, the interaction between the fringes-caustic and caustic irradiance is studied using a predator-prey model, which leads to a logistic-type differential equation with nonlinear harvesting. The stability analysis of this equation is in good agreement with the theoretical and experimental results.

Bridge damage identification based on synchronous statistical moment theory of vehicle–bridge interaction

AbstractConsidering the weak noise resistance and low identification efficiency of traditional bridge damage identification methods, a data‐driven approach based on synchronous statistical moment theory and vehicle–bridge interaction vibration theory is proposed. This method involves two main steps. First, a two‐axle test vehicle is used to collect acceleration response signals synchronously from adjacent designated measurement points while stationary. This operation is repeated to calculate the second‐order statistical moment curvature (SOSMC) difference of entire bridge points corresponding signals in different states. By comparing with the reference value, the preliminary damage location of the bridge can be obtained. Second, the first‐order modal shape curve is constructed using the second‐order statistical moment (SOSM). The refined identification of bridge damage is then based on an improved direct stiffness back calculation of the bridge's stiffness. This article proposes the synchronization theory for the first time and combines it with the statistical moment clustering method, forming an innovative approach to obtaining structural vibration modes. The effectiveness of this method has been well validated through numerical simulations with different parameters and on‐site bridge tests. The research results indicate that SOSMC indicators have better noise resistance and higher recognition efficiency in identifying damage locations, compared to modal curvature and flexibility curvature indicators. Additionally, compared to transfer rate and random subspace methods, the SOSM method results in smaller error and higher identification efficiency.

Crack detection and localization in composite plates by intersection of first three normalized mode shape curves from experimental modal analysis

Crack detection and localization in composite plates by intersection of first three normalized mode shape curves from experimental modal analysis

Investigation of structural and TL kinetic parameters of smartphone screen protector glasses for applications in retrospective dosimetry

The study evaluated the structural and thermoluminescence (TL) kinetic parameters of smartphone screen protector glasses in order to use them for post-accident dose reconstruction from unplanned nuclear events. The fact that most individuals use mobile phones in working environments including nuclear power plant sites, served as the impetus for the study. The TL glow curves indicate the physical properties of the defects involved in the luminescence process; therefore, they have been analyzed to study the TL kinetic parameters by employing peak shape, initial rise and glow curve deconvolution method within the dose ranges from 2 to 50 Gy. The geometric factor (μg) ranges between 0.46 and 0.56, suggesting that Chen's general-order method can be used to compute the kinetic parameters, including activation energy (E), frequency factor (s) and trap lifetime (τ). The examined trapping parameters (E = 0.33–0.57 eV, s = 5.22E+03–8.65E+06 s−1 for peak shape and E = 0.36–0.96 eV, s = 2.90E+04–1.88E+11 s−1 for initial rise methods) suggest promise for TL dosimetry applications. Additionally, the observed lifetime (τ = 4.88E+5 s) implies the feasibility of dose reconstruction even several days after an accident, making it suitable for retrospective dosimetry. Micro-Raman spectroscopy revealed a clear correlation between increasing gamma radiation dose and microstructural damage. The analysis of intensity ratio (ID/ISi) for other components to silica, along with the area of deconvoluted micro-Raman spectra in high-frequency regions, indicated dose-dependent structural modifications and internal defect annealing. Further confirmation of structural alterations within the studied dose range was obtained through the analysis of crystallite size (Lc), dislocation density (δ), lattice strain (ɛ) and FWHM (Full Width at Half Maximum) from XRD (X-ray diffraction) patterns. These findings collectively suggest the potential of smartphone screen protector glass as a viable material for emergency dosimetry applications.

Response to Discretising and validating Keyfitz' entropy for any demographic classification

Abstract In recent years, demographers have parsed variation in survivorship into two distinct components: the shape and the pace of ageing. The pace of ageing is defined by measures of longevity such as mean life expectancy or maximum longevity, whereas measures of the shape of ageing attempt to classify different shapes of the survivorship curve. We recently published a paper pointing out that a commonly used discretization of a shape measure, Keyfitz' entropy, does not correctly classify survivorship curves into negatively and positively senescing curves (de Vries et al., 2023). In that paper, we also suggested an alternative, accurate discrete‐time version of Keyfitz' entropy. de Vries et al. (2023) ended with two open questions, both of which have been answered by Giaimo (2024) now: (1) Can a discrete‐time entropy measure of survivorship be generalized beyond age‐based population models? Giaimo (2024) introduce a new formula that achieves this. (2) Will a discretization of Keyfitz' derivation of his measure as the elasticity of lifespan to a uniform change in mortality lead to the same formula as a discretization of Keyfitz' result? Giaimo (2024) answers: no. Here, we briefly discuss the implications of the results obtained by Giaimo (2024), and the implementation of his new formula into the Rpackage Rage, which is widely used for comparative demographic studies. We showcase the strength of the new method by reanalysing a comparison of Keyfitz' entropy to another shape measure. We find that the comparison is significantly altered by using Giaimo's new Keyfitz' formula. This example strengthens Giaimo's (2004) words of warning in approaching discretizations with attentiveness.

Optimization of an anatomically and electrically detailed rodent subthalamic nucleus neuron model.

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is an effective treatment for Parkinson's disease, but its mechanisms of action remain unclear. Detailed multicompartment computational models of STN neurons are often used to study how DBS electric fields modulate the neurons. However, currently available STN neuron models have some limitations in their biophysical realism. In turn, the goal of this study was to update a detailed rodent STN neuron model originally developed by Gillies and Willshaw in 2006. Our design requirements consisted of explicitly representing an axon connected to the neuron and updating the ion channel distributions based on the experimental literature to match established electrophysiological features of rodent STN neurons. We found that adding an axon to the STN neuron model substantially altered its firing characteristics. We then used a genetic algorithm to optimize biophysical parameters of the model. The updated model exhibited spontaneous firing, action potential shape, hyperpolarization response, and frequency-current curve that aligned well with experimental recordings from STN neurons. Subsequently, we evaluated the general compatibility of the updated biophysics by applying them to 26 different STN neuron morphologies derived from three-dimensional anatomical reconstructions. The different morphologies affected the firing behavior of the model, but the updated biophysics were robustly capable of maintaining the desired electrophysiological features. The new STN neuron model developed in this work offers a valuable tool for studying STN neuron firing properties and may find application in simulating STN local field potentials and analyzing the effects of STN DBS.NEW & NOTEWORTHY This study presents an anatomically and biophysically realistic rodent STN neuron model. The work showcases the use of a genetic algorithm to optimize the model parameters. We noted a substantial influence of the axon on the electrophysiological characteristics of STN neurons. The updated model offers a valuable tool to investigate the firing of STN neurons and their modulation by intrinsic and/or extrinsic factors.

Tilted biorthogonal ensembles, Grothendieck random partitions, and determinantal tests

We study probability measures on partitions based on symmetric Grothendieck polynomials. These deformations of Schur polynomials introduced in the K-theory of Grassmannians share many common properties. Our Grothendieck measures are analogs of the Schur measures on partitions introduced by Okounkov (Sel Math 7(1):57–81, 2001). Despite the similarity of determinantal formulas for the probability weights of Schur and Grothendieck measures, we demonstrate that Grothendieck measures are not determinantal point processes. This question is related to the principal minor assignment problem in algebraic geometry, and we employ a determinantal test first obtained by Nanson in 1897 for the 4×4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\ imes 4$$\\end{document} problem. We also propose a procedure for getting Nanson-like determinantal tests for matrices of any size n≥4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\ge 4$$\\end{document}, which appear new for n≥5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\ge 5$$\\end{document}. By placing the Grothendieck measures into a new framework of tilted biorthogonal ensembles generalizing a rich class of determinantal processes introduced by Borodin (Nucl Phys B 536:704–732, 1998), we identify Grothendieck random partitions as a cross-section of a Schur process, a determinantal process in two dimensions. This identification expresses the correlation functions of Grothendieck measures through sums of Fredholm determinants, which are not immediately suitable for asymptotic analysis. A more direct approach allows us to obtain a limit shape result for the Grothendieck random partitions. The limit shape curve is not particularly explicit as it arises as a cross-section of the limit shape surface for the Schur process. The gradient of this surface is expressed through the argument of a complex root of a cubic equation.

Euler Bézier spirals and Euler B-spline spirals

Euler spirals have linear varying curvature with respect to arc length and can be applied in fields such as aesthetics pleasing shape design, curve completion or highway design, etc. However, evaluation and interpolation of Euler spirals to prescribed boundary data is not convenient since Euler spirals are represented by Fresnel integrals but with no closed-form expression of the integrals. We investigate a class of Bézier or B-spline curves called Euler Bézier spirals or Euler B-spline spirals which have specially defined control polygons and approximate linearly varying curvature. This type of spirals can be designed conveniently and evaluated exactly. Simple but efficient algorithms are also given to interpolate G1 boundary data by Euler Bézier spirals or cubic Euler B-spline spirals.

Comparison of machine learning and deep learning models for the assessment of rondo wine grape quality with a hyperspectral camera

Hyperspectral images provide rich spectral/spatial data and have shown remarkable performance in precision viticulture. Standardized data-processing methods are necessary to reduce the dimensionality and to identify powerful wavelengths. Toward this goal, we evaluated and compared the performance and novel-wavelength-identification ability of five renowned machine learning models: the linear models Ridge and LASSO, a 1D + 2D convolutional neural network (1D +2D CNN) non-linear model, a gradient boosting decision tree (GBDT) using XGBoost as an ensemble model, and an explainable boosting machine (EBM) followed by support vector regression (SVR) as a hybrid model. The model evaluations were conducted using leave-one-out cross-validation (LOOCV) as we sought to clarify the best-fitted machine learning model. Our results demonstrated that Ridge, LASSO, showed better performance with relatively high accuracy but were weak as a wavelength identifier. GDBT-XGBoost showed considerable prediction power and wavelength identification. EBM-SVM emerged as the most powerful model, demonstrating exceptional stability and clear wavelength classification even for destructive measurements under varying environmental stresses across Rondo's growth stages. The combined approach of 1D + 2D CNN algorithms was advantageous to handle the dynamic shapes of spectral curve and horizontal shift of the wavelengths obtained from outdoor data acquisition, and notably, it showed the highest accuracy to predict the brix and pH of wine grapes for both indoor and outdoor sensings. But the combined effects of 1D and 2D CNN algorithms were difficult to clarify the importance of spectral features for the brix and pH prediction. The integrated machine learning models with dimensionality reduction, and proper image acquisition can increase the model's accuracy. The common absorption peaks were observed in the near-infrared region of 700 nm and 900 nm. Those wavelengths should be considered for the development of low-cost sensing platforms with fewer bands. Wavelengths over 900 nm are also important to develop outdoor sensing platforms.

Predicting pump-turbine characteristic curves by theoretical models based on runner geometry parameters

The characteristic curve of a pump-turbine is the essential data for calculating the hydraulic transient processes of a pumped storage power station. However, this curve is often unavailable during the preliminary design stage of pumped storage power stations. The shape of the characteristic curve directly influences the transient guarantee parameters. To date, adjusting the runner geometry to control the characteristic curve's shape for improving hydraulic transients remains a challenging issue. This paper proposes a model for predicting the characteristic curve that correlates its shape with the runner's geometric parameters. Considering the bidirectional flow in pump-turbines, two sets of governing equations are derived separately for the centripetal and centrifugal flow conditions. The governing equations for the unit discharge curve and the unit torque curve are constructed based on the energy equation and torque equation, respectively. Each term in these equations is subsequently organized into the expressions involving the runner's geometric parameters and unit parameters. To make the equations solvable, several sets of feature points are introduced. Based on the approach to obtain the feature points, an experiment/CFD (Computational Fluid Dynamics)-based prediction method and a statistics-based prediction method are proposed. Verifications using manufacturer-measured curves show that the experiment/CFD-based method is well-suited for model test acceleration and characteristic curve repair due to its higher prediction accuracy and availability, while the statistics-based method is more suitable for borrowing similar curve data during the power plant's preliminary design phase or rapidly predicting the corresponding characteristic curves during runner design. This work establishes a theoretical basis for improving hydraulic transient guarantee parameters by runner design optimization.

Classification and evolution of bifurcation curves of semipositone problem with Minkowski-curvature operator and its applications

In this paper, we study the classification and evolution of bifurcation curves of semipositone problem with Minkowski-curvature operator{−(u′/1−u′2)′=λf(u), in (−L,L),u(−L)=u(L)=0,where λ,L>0, f∈C2(0,∞), and the following conditions (H1)–(H2) hold:(H1)there exists β>0 such that (β−u)f(u)<0 for u>0 and u≠β.(H2)Let F(u)≡∫0uf(t)dt. Then F:[0,∞)⟶R is continuous and differentiable for u>0. And there exists η>0 such that (η−u)F(u)<0 for u>0 and u≠η. Notice that we allow f(0+)=−∞. In particular, we further obtain the exact shapes of the bifurcation curve as f is convex or concave. Finally, we apply these results in several problems.

Evaluation of Sabkha Soil Bearing Capacity by Plate Load Test in Al Muthanna Province

For projects such as airports and road paving, an appropriate foundation must be developed in Sabkha soil, which requires a trustworthy assessment of soil-bearing capacity. When heavy traffic is expected to result in substantial wheel loads throughout pavement construction and maintenance, the plate load test helps solve these issues with subgrade and sub-base layer design. This work aims to investigate and assess the geotechnical behavior regarding soil strata from one area in southern Iraq: Sabkha. Conversely, a comparison is made between subgrade response modulus and soil-bearing capacity determined by field plate load tests and traditional laboratory investigations. The data demonstrated that the values related to Ks in the consolidation test rose as a ratio of pre-consolidation pressure of 45% and dramatically dropped with an increase in applied stress that is vertically applied below pre-consolidation stress. Furthermore, PLT data demonstrated that when pressure was applied, the modulus of the subgrade reaction did not follow a regular pattern. At the beginning of the loaded stage, after the pre-consolidation stress, Ks values at testing points 2 and 3 were high. After that, Ks abruptly decreased, particularly when the applied pressure surpassed the pre-consolidation stress before being constant again. A detailed discussion is given on the effects of stress distribution and test conditions on the elasticity stress curve's shape and the subgrade reaction modulus.

Small-Scale Cosmology Independent of the Standard Model

‘Small-scale cosmology’ is a theory designed to incorporate the linear redshift versus distance relation, which is inferred from observations, into the theoretical framework independent of the global Robertson–Walker–Friedman (RWF)-type models. The motivation behind this is that the RWF cosmological models, based on the assumptions of homogeneity and a constant matter density, as well as the concept of expanding space inherent to them are not applicable on the scales of observations from which the linear Hubble law is inferred. Therefore, explaining the Hubble law as the small redshift limit of the RWF model or as an effect of expanding space is inconsistent. Thus, the Hubble linear relation between the redshift of an extragalactic object and its distance should be considered an independent law of nature valid in the range of the distances where the RWF cosmology is not valid. In general, the theory, based on that concept, can be developed in different ways. In the present paper, ‘small-scale cosmology’ is formulated as a theory operating in the (redshift–object coordinates) space, which allows developing a conceptual and computational basis of the theory along the lines of that of special relativity. In such a theory, the condition of invariance of the Hubble law with respect to a change in the observer acceleration plays a central role. In pursuing this approach, the effectiveness of group theoretical methods is exploited. Applying the Lie group method yields transformations of the variables (the redshift and space coordinates of a cosmological object) between the reference frames of the accelerated observers. In this paper, the transformations are applied to studying the effects of the solar system observer acceleration on the observed shape, distribution and rotation curves of galaxy clusters.