Dimensional Curve Research Articles

Analysis of the transverse vibration of a multistepped FGM beam resting on a Winkler foundation in a thermal environment and carrying concentrated masses

This paper examines a novel case study involving the free vibration of a stepped FGM beam-mass system resting on elastic foundations and subjected to a nonlinear or uniform thermal load. The present study examines the complex interaction of thermal effects on dynamic behavior by varying the cross-section and length ratios, material parameters and mass magnitudes. After adopting Euler-Bernoulli's theory, the dynamic behavior of non-uniform FGM beams was investigated using the generalized finite element method (GFEM) and the Rayleigh quotient finite element method (RQFEM). In line with the objective set, relevant results derived from parametric studies, showcasing accentuated variation in dimensional frequency curves and bending moments, have been highlighted and discussed.

On split-octonionic curves

Abstract In this paper, we first define the vector product in Minkowski space $\mathbb{R}_{4}^{7}$, which is identified with the space of spatial split-octonions. Next, we derive the $G_{2}-$ frame formulae for a seven dimensional Minkowski curve by using the spatial split-octonions and the vector product. We show that Frenet–Serret formulas are satisfied for a spatial split octonionic curve. We obtain the congruence of two spatial split octonionic curves and give relationship between the $G_{2}-$ frame and Frenet–Serret frame. Furthermore, we present the Frenet–Serret frame with split octonions in $\mathbb{R}_{4}^{8}$. Finally, we give illustrative examples with Matlab codes.

A biogenic organic molecule involved in the formation of secondary organic aerosols: Microwave and millimeter-wave spectroscopy of 3-methylcatechol backed by quantum chemistry

3-methylcatechol (3MC) is a molecule of environmental interest due to its presence in the atmosphere during biomass burning events, leading to the formation of secondary organic aerosols. This paper goes one step further than the paper from A.S. Hazrah et al. (2022) [10]. A three-dimensional torsional potential energy surface was determined, confirming the existence of three rotamers for 3MC. One dimensional potential energy curves along the rotation of the methyl group were computed and fitted to estimate the barrier height in each conformer. Experiments were performed at low temperature in the microwave domain (2−20GHz range) and, for the first time, in the millimeter-wave domain (70−110GHz range) at T=323K with a specially designed heated absorption cell. The rotational linelist was fitted to provide updated spectroscopic parameters for the two 3MC conformers of lowest energies. In particular, the A−E splitting is observed in the microwave region for both conformers while in the millimeter-wave region, it is only seen for the conformer of the lowest energy.

Generalized weighted permutation entropy analysis of satellite hot-pixel time series in Brazilian biomes

In this work we analyze hot-pixel satellite data, proxy for natural and anthropogenic vegetation and forest fires, using recently proposed method Generalized weighted permutation entropy (GWPE). The current analysis of data from 2002 to 2022 for six Brazilian biomes sheds new light on differences among the biomes in terms of ordinal pattern entropy, for both small and large fluctuations. It is found that for all biomes large fluctuations in fire temporal series show higher complexity level than small fluctuations, small fluctuations being more predictable as indicated by lower entropy values. Moreover, for fire sensitive biomes Amazon and Atlantic Forest the three dimensional complexity entropy curves in the complexity-entropy-scale causality box (CESCB) are rather similar (indicating similar dynamics for both small and large fluctuations), as well as for fire dependent biomes Pantanal and Pampa, while fire independent Caatinga biome shows different, distinct behavior. Finally, the similarity in lower parts of the CESCB curves (corresponding to small fluctuations) between Amazon and Cerrado reflects the changes of fire dynamics due to human activities.

Anisotropic regularity for elliptic problems with Dirac measures as data

We study the Possion problem with singular data given by a source supported on a one dimensional curve strictly contained in a three dimensional domain. We prove regularity results for the solution on isotropic and on anisotropic weighted spaces of Kondratiev type. Our technique is based on the study of a regularized problem. This allows us to exploit the local nature of the singularity. Our results hold with very few smoothness hypotheses on the domain and on the support of the data. We also discuss some extensions of our main results, including the two dimensional case, sources supported on closed curves and on polygonals.

On Hybrid Curves

In this paper, we first define the vector product in a special analog Minkowski Geometry (R^3,) which is identified with the space of spatial hybrids. Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product. However, we present the Frenet-Serret frame formulae of a non-lightlike hybrid curve in R^4 and an illustrative example for all theorems of the paper with MATLAB 2016a codes.

Exponential Networks, WKB and Topological String

We propose a connection between 3d-5d exponential networks and exact WKB for difference equations associated to five dimensional Seiberg-Witten curves, or equivalently, to quantum mirror curves to toric Calabi-Yau threefolds $X$: the singularities in the Borel planes of local solutions to such difference equations correspond to central charges of 3d-5d BPS KK-modes. It follows that there should be distinguished local solutions of the difference equation in each domain of the complement of the exponential network, and these solutions jump at the walls of the network. We verify and explore this picture in two simple examples of 3d-5d systems, corresponding to taking the toric Calabi-Yau $X$ to be either $\mathbb{C}^3$ or the resolved conifold. We provide the full list of local solutions in each sector of the Borel plane and in each domain of the complement of the exponential network, and find that local solutions in disconnected domains correspond to non-perturbative open topological string amplitudes on $X$ with insertions of branes at different positions of the toric diagram. We also study the Borel summation of the closed refined topological string free energy on $X$ and the corresponding non-perturbative effects, finding that central charges of 5d BPS KK-modes are related to the singularities in the Borel plane.

Derivation of Optimal Two Dimensional Rule Curve for Dualistic Reservoir Water-Supply System

In arid and semi-arid regions particularly vulnerable to climate change, optimizing the long-term operation of multi-purpose reservoirs is paramount. This study derived an optimum two-dimensional rule curve to jointly operate the parallel reservoirs of Mosul and Dukan, Northern Iraq. A hybridized optimization technique combining conventional dynamic programming with the shuffled complex evolution algorithm (SCE-UA) was developed to solve this problem. The results showed that the proportion of normal water supply areas increased from the beginning of the flood season (October) to its highest levels in April (58.77% of the total water supply area). The proportion decreased to its lowest in September (25.04% of the total water supply area). The newly derived 2D rule cure was compared with the current operation policy and was found to optimize the amount of water shortage by 21.1% during the operational period. It also reduced the shortage period and avoided catastrophic water shortages during droughts. In addition, the developed model optimized the amounts of water more than the joint water requirements, suffering from a significant deficit in meeting the demand during some months of the operational years. As a result, the storage in each reservoir was improved and thence can be adapted to face water shortages during future climate changes. This study proved the new hybridized model's applicability and can serve as a tool for sustainable water management. Doi: 10.28991/CEJ-2023-09-07-016 Full Text: PDF

Fluid topology optimization and additive manufacturing of a liquid atomizer using an extensive number of grid points

Additive manufacturing (AM) can fabricate complicated shapes and is useful when manufacturing topology optimized shapes. Fluid parts often consists of three dimensional curves that are suitable for AM fabrication. However, the application of fluid topology optimization and AM has not been investigated yet. However, modeling and solving an optimization problem have not been investigated for a real industrial fluid topology optimization problem of AM parts with tiny channels, i.e., a liquid atomizer which is equipped with an aero-engine fuel injector. In order to reduce computation time, which is an important issue in real industrial problem, the instantaneous sensitivity approximation method is used as a topology optimization method. The optimized part exhibited a reduction in pressure loss compared to that of a conventional part.

On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators

Horadam sequence is a general recurrence of second order in the complex plane, depending on four complex parameters (two initial values and two recurrence coefficients). These sequences have been investigated over more than 60 years, but new properties and applications are still being discovered. Small parameter variations may dramatically impact the sequence orbits, generating numerous patterns: periodic, convergent, divergent, or dense within one dimensional curves. Here we explore Horadam sequences whose orbit is dense within a 2D region of the complex plane, while the complex argument is uniformly distributed in an interval. This enables the design of a pseudo-random number generator (PRNG) for the uniform distribution, for which we test periodicity, correlation, Monte Carlo estimation of π, and the NIST battery of tests. We then calculate the probability distribution of the radii of the sequence terms of Horadam sequences. Finally, we propose extensions of these results for generalized Horadam sequences of third order.

Investigation on the mechanical properties of shale subjected to different conditions based on nanoindentation experiments and numerical simulation

Nano indentation has become an important means to study the mechanical properties of rock because of its nondestructive and high efficiency. In this work, the Weibull distribution function is used to statistically analyze the nanoindentation test results and to analyze them mechanically and parametrically. The indentation process was simulated using ABAQUS to investigate the effect of semi-through cracks at the indentation on the indentation results. The experimental and simulated results were also analyzed using the dimensional analysis method. The results show that the elastic modulus, hardness and fracture toughness are positively correlated. The correlation between hardness and fracture toughness is poor. In the simulated indentation experiment, the number, depth, distance and Angle of semi-penetrating cracks have different effects on the indentation results. The proportional coefficients of dimensional analysis fitting curves are 0.464, 0.464, 0.457 and 0.462, respectively, which means that the number and depth of cracks have a great influence on the experimental results.

Structure of the set of Borel exceptional vectors for entire curves. II

We have obtained a description of structure of the sets of Picard and Borel exceptional vectors for transcendental entire curve in some sense. We consider only $p$-dimensional entire curves with linearly independent components without common zeros.In particular, the set of Borel exceptional vectors together with the zero vector is a finite union of subspaces in $\mathbb{C}^{p}$ of dimension at most $p-1$. Moreover, the sum of their dimensions does not exceed $p$ if anypairwise intersection of the subspaces contains only the zero vector. A similar result is also valid for the set of Picardexceptional vectors.Another result shows that the structure of the set of Borel exceptional vectors for an entire curve of integer orderdiffers somewhat from the structure of such a set for an entire curve of non-integer order.For a transcendental entire curve $\vec{G}:\mathbb{C}\to \mathbb{C}^{p}$ with linearly independent components and without common zeros having non-integer or zero order the set of Borel exceptional vectors together with the zero vector is a subspace in $\mathbb{C}^{p}$ of dimension at most $p-1$.
 However, the set of Picard exceptional vectors does not possess this property. We propose two examples of entire curves.The first example shows the set of Borel exceptional vectors together with the zero vector for $p$-dimensional entire curve of integer order isunion of subspaces of dimension at most $p-1$ such that the total sum of these dimensions does not exceed $p$ and intersection of any pair of these subspaces contains only zero vector. The set of Picard exceptional vectors for the curve has the same property.In the second example, we construct a $q$-dimensional entire curve of non-integer order for which the set of Borel exceptional vectors together with the zero vector is a subspace in $\mathbb{C}^{q}$ of dimension at most $q-1$ and the set of Picard exceptional vectors together with the zero vectordo not have the property. This set is a union of some subspaces.

The quantitative role of chemical species in multi-route reaction: A mathematical paradigm

In the field of chemical kinetics, many researchers are familiar with the idea of mathematical modeling in terms of ordinary differential equations. However, the statistical analysis on the involvement of the species (chemical component) and their role at each step and during their available routes covers the hierarchy of mathematical models in applied and computational mathematics. This paper will focus on the participation of chemical species and the invariant region of the reaction mechanism. The invariant region gives an idea of where invariant manifold (low dimensional manifold) lies when applying some model reduction technique. Here, a computational technique ‘Spectral Quasi Equilibrium Manifold’ (SQEM) gives accurate grid points to achieve the required dimensional curves without affecting the accuracy of the system.

Efficient estimation of material property curves and surfaces via active learning

The relationship between material properties and independent variables such as temperature, external field or time, is usually represented by a curve or surface in a multi-dimensional space. Determining such a curve or surface requires a series of experiments or calculations which are often time and cost consuming. A general strategy uses an appropriate utility function to sample the space to recommend the next optimal experiment or calculation within an active learning loop. However, knowing what the optimal sampling strategy to use to minimize the number of experiments is an outstanding problem. We compare a number of strategies based on directed exploration on several materials problems of varying complexity using a Kriging based model. These include one dimensional curves such as the fatigue life curve for 304L stainless steel and the Liquidus line of the Fe-C phase diagram, surfaces such as the Hartmann 3 function in 3D space and the fitted intermolecular potential for Ar-SH, and a four dimensional data set of experimental measurements for BaTiO3 based ceramics. We also consider the effects of experimental noise on the Hartmann 3 function. We find that directed exploration guided by maximum variance provides better performance overall, converging faster across several data sets. However, for certain problems, the trade-off methods incorporating exploitation can perform at least as well, if not better than maximum variance. Thus, we discuss how the choice of the utility function depends on the distribution of the data, the model performance and uncertainties, additive noise as well as the budget.

Development of prediction model through linear multiple regression for the prediction of longitudinal stiffness of embroidered fabric

Embroidery through computer aided semi-automatic machines is one of the most widely used option for the surface ornamentation of apparel fabrics at present. Since the embroidery process includes addition of certain amount of embroidery-threads depending upon the design motif, it is quite obvious that basic physical and functional properties of fabric are subject to change. It is therefore important to develop an algorithm or empirical equation for proper prediction of the properties of the embroidered fabric, relevant to its required end-use in apparel industry. In this context, an effort has been made to determine a prediction equation through linear multiple regressions for the prediction of longitudinal stiffness of embroidered fabric in terms of flexural rigidity in warp direction of the base fabric, considering the input parameters as warp-way flexural rigidity of the base fabric, breaking load and linear density of the embroidery thread, stitch density, average stitch length and average stitch angle of the embroidery design. The final Prediction model is statistically verified taking new embroidery samples of different varieties. It is found that the model can predict with a very satisfactory level of accuracy. Also, the influences of the embroidery parameters in this context have been analyzed through the corresponding regression coefficients and the three dimensional (3D) surface curves. Stitch density has been emerged as the most influential parameter, followed by the stitch length and the stitch angle.

Thermodynamic modeling of comprehensive two dimensional gas chromatography isovolatility curves for second dimension retention indices based analyte identification

A method to thermodynamically model the alkane isovolatility curves of a comprehensive two dimensional gas chromatography (GC × GC) separation is presented. This method omits all instrument modifications, additional chromatogram collection, or method alterations which typical isovolatility curve generation requires. Provided that the thermodynamic indices of reference alkanes are available, chromatographers only need to specify the GC × GC method parameters of their separation to output the isovolatility curves. The curves can then be used alongside reference retention indices to generate two dimensional retention times for each analyte. Agreement between the modeled and experimental retention times provides a secondary mechanism for compound identification, supporting the results of a mass spectral search. The technique was used to model the retention times of a GC × GC separation of aromatic hydrocarbons, achieving an average first dimension retention time modeling error of 11 s and an average second dimension retention time modeling error of 0.09 s. Retention indices modeled retention times provide a simpler analyte identification procedure compared to conventional two dimensional retention indices matching.

RADIATION MEASUREMENT OF RADIOISOTOPE IN MINERAL DEPOSIT AT SUBDISTRICT OF MIDDLE KUPANG WEST TIMOR ISLAND INDONESIA

The general objective of this work was investigation of radioisotope distribution and accumulation center in mineral deposit at sub-district of Middle Kupang West Timor Island Indonesia. The purposes of research were: to map of radioisotope distribution in the mineral deposit, to estimate area of radioisotope accumulation center in the mineral deposit, to establish range of nuclear radiation counts in the center region of radioisotope content in mineral deposit. The general methods used in this research were observation, survey, mapping, analysis, and interpretation. Procedures detail of research consists of: observe and identify the potential region and plot gridding, calibrate equipment necessary, measure background count in around of survey location and nuclear radiation in the survey location, plot of three dimensions curve and contour after corrected by background count. Based on geology information or geology data (drilling data) three depth levels determined (about 20 m, 40 m and 60 m), Radiation powers were calculated for estimation of accumulation center of radioisotope in deposit mineral, and contour and three dimensions curves of radiation power of radioisotope in deposit mineral were plotted. Results: Based on three dimensional curves and contour map (radiation counts and radiation powers on three levels) of radioisotope in mineral deposit respectively was distributed on area 3.00 x 106 m2, and 1.56 x 104 m2. The interval of radiation counts of radioisotope in mineral deposit was 10 counts per minute-137 counts per minute.
 Keywords: Radiation, measurement, radioisotope, mineral, deposit

A Proof for the Birch Swinnerton-Dyer Conjecture

The Birch Swinnerton-Dyer Conjecture states that the number of rational points on an elliptic curve are infinite. This paper develops the logical formalism for a reinforcement learning system embedded with a quantum search algorithm. The formalism proves the rational points on high dimensional elliptical curves are infinite.

Steady-state regimes prediction of a multi-degree-of-freedom unstable dynamical system coupled to a set of nonlinear energy sinks

Abstract A general method to predict the steady-state regimes of a multi-degree-of-freedom unstable vibrating system (the primary system) coupled to several nonlinear energy sinks (NESs) is proposed. The method has three main steps. The first step consists in the diagonalization of the primary underline linear system using the so-called biorthogonal transformation. Within the assumption of a primary system with only one unstable mode the dynamics of the diagonalized system is reduced ignoring the stable modes and keeping only the unstable mode. The complexification method is applied in the second step with the aim of obtaining the slow-flow of the reduced system. Then, the third step is an asymptotic analysis of the slow-flow based geometric singular perturbation theory. The analysis shows that the critical manifold of the system can be reduced to a one dimensional parametric curve evolving in a multidimensional space. The shape and the stability properties of the critical manifold and the stability properties of the fixed points of the slow-flow provide an analytical tool to predict the nature of the possible steady-state regimes of the system. Finally, two examples are considered to evaluate the effectiveness and advancement of the proposed method. The method is first applied to the prediction of the mitigation limit of a breaking system subject to friction-induced vibrations coupled to two NESs, and next an airfoil model undergoing an aeroelastic instability coupled to a NESs setup (from one to four) is discussed. Theoretical results are compared, for validation purposes, to direct numerical integration of the system. The comparisons show good agreement.

Composite generation of independently controllable multiple three-dimensional vector focal curve beams

We propose an approach for simultaneously shaping multiple three dimensional (3D) vector curve beams. The intensity distribution and polarization state variation of each 3D vector curve beam can be tuned along arbitrary prescribed trajectories. The scheme is based on the coaxial superposition of the orthogonally polarized 3D base vector curve beams through non-iterative holographic 3D beam shaping technique. In particular, the hybrid 3D vector curve beams array is also generated with identical depth range. The transversal position of each vector beam can be governed independently. Moreover, the multiplexing of 3D vector beams is realized with different depth ranges in the focal region along the beam propagation. The numerical results are identical to the experiments. This method will be benefit to the trapping and transportation of particles.