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4. Time series analysis of duty cycle induced randomness in thermal lens systemMohanachandran Nair Sindhu Swapna, 2020, original scientific article Abstract: The present work employs time series analysis, a proven powerful mathematical tool, for investigating the complex molecular dynamics of the thermal lens (TL) system induced by the duty cycle (C) variation. For intensity modulation, TL spectroscopy commonly uses optical choppers. The TL formation involves complex molecular dynamics that vary with the input photothermal energy, which is implemented by varying the duty cycle of the chopper. The molecular dynamics
is studied from the fractal dimension (D), phase portrait, sample entropy (S), and Hurst exponent (H) for different duty cycles. The increasing value of C is found to increase D and S, indicating that the system is becoming complex and less deterministic, as evidenced by the phase portrait analysis. The value of H less than 0.5 conforms the evolution of the TL system to more anti-persistent nature with C. The increasing value of C increases the enthalpy of the system that appears as an increase in full width at half maximum of the refractive index profile. Thus the study establishes that the sample entropy and thermodynamic entropy are directly related.
Keywords: Time series analysis
Fractal analysis
Photothermal lens spectroscopy
Fractal dimension
Hurst exponent
Sample entropy
Published in RUNG: 05.07.2022; Views: 2089; Downloads: 0
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5. Hidden periodicity in Stripe 82 with Saraswati supercluster—a fractal analysisVimal Raj, Mohanachandran Nair Sindhu Swapna, Sankaranarayana Iyer Sankararaman, 2021, original scientific article Abstract: The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently
reported Saraswati supercluster and the Stripe 82 region containing it as an example. The report
of 120 Mpc periodicity in the Abell galaxy clusters by power spectrum analysis is the motivation
behind the study. The power spectral analysis across the central part of the Stripe 82 region
shows a periodic variation of 3.09° or 71 Mpc in fractal dimension whereas an average angular
periodicity of 3.45° or 94 Mpc is observed across the Stripe 82 region. This refers to the
periodicity of complexity or cluster density of galaxy distribution. The texture of the distribution
pattern understood through lacunarity analysis indicates a near symmetric distribution. Fractal
dimensions like box-counting dimension, information dimension and correlation dimension are
also found through multifractal analysis. While the information dimension tells about the
distribution density of galactic points, the correlation dimension details the distribution of
galaxies in the neighbourhood
Keywords: galaxy distribution, fractal analysis, multifractals, lacunarity, Saraswati supercluster, Stripe 82
Published in RUNG: 04.07.2022; Views: 1930; Downloads: 0
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7. Evolution of fractal dimension in pulsed laser deposited MoO3 film with ablation time and annealing temperatureMohanachandran Nair Sindhu Swapna, 2021, original scientific article Abstract: The multifractal analysis is a potential method for assessing thin flm surface morphology and its changes due to diferent
deposition conditions and post-deposition treatments. In this work, the multifractal analysis is carried out to understand the
surface morphology—root mean square (RMS) surface roughness—of nanostructured MoO3 flms prepared by pulsed laser
deposition technique by varying the ablation time and post-deposition annealing. The XRD analysis shows the evolution of
crystalline nature with annealing temperature. The XRD pattern of all the annealed flms shows the characteristic peak of
the orthorhombic MoO3 phase. The FESEM and AFM analysis reveals the morphological modifcation with ablation time
and annealing temperature. The multifractal analysis of the AFM images shows that the box—counting, information and
correlation dimension varies with the annealing temperature. The study also reveals the inverse relation between the fractal
dimension and the RMS surface roughness due to the annealing induced particle size variation and reorientation. The fractal
dimension’s evolution in the pulsed laser deposited MoO3 flm with ablation time and annealing temperature is also investigated. Thus, the study reveals the potential of multifractal analysis in the thin flm surface characterizatio
Keywords: Multifractal analysis · Pulsed laser deposition · Molybdenum oxide · Atomic force microscopy · Fractal
dimension
Published in RUNG: 04.07.2022; Views: 2046; Downloads: 0
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8. Investigation of Fractality and variation of fractal dimension in germinating seedMohanachandran Nair Sindhu Swapna, SREEJYOTHI S, Sankararaman S, 2020, original scientific article Abstract: The fractal analysis has now been recognized as a potential mathematical tool in analyzing complex structures. The present work reports not only the fractal nature of Vigna radiata seed analyzed with the help of Field Emission Scanning Electron Microscopic images but also the variation of fractal dimension (FD) in a germinating seed. The variation of FD during germination in different media—water, salt, and diesel soot with carbon nanoparticles (CNPs)—is studied using the box-counting technique. The study is the first report of the fractality of seed. Irrespective of the media, the FD attains a maximum value on the day of germination and decreases after that. The time (T) for achieving maximum FD varies with the nature of stress. In the study, when the CNPs of diesel soot lower the T value, the salt raises the T value with respect to the control set. The Fourier Transform Infrared analysis of the seeds germinating in different media shows an increased rate of protein formation during the initial stage of germination and a steady state after that. In conjunction with the literature, the variation in the amino nitrogen, soluble nucleotide—RNA, and protein content of the seed during the initial days of germination gets reflected in its FD.
Keywords: fractal analysis, seed germination, Vigna radiata
Published in RUNG: 04.07.2022; Views: 1968; Downloads: 0
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9. Fractal and time-series analyses based rhonchi and bronchial auscultation: A machine learning approachMohanachandran Nair Sindhu Swapna, 2022, original scientific article Abstract: Objectives: The present work reports the study of 34 rhonchi (RB) and
Bronchial Breath (BB) signals employing machine learning techniques, timefrequency, fractal, and non-linear time-series analyses. Methods: The timefrequency analyses and the complexity in the dynamics of airflow in BB
and RB are studied using both Power Spectral Density (PSD) features and
non-linear measures. For accurate prediction of these signals, PSD and nonlinear measures are fed as input attributes to various machine learning
models. Findings: The spectral analyses reveal fewer, low-intensity frequency
components along with its overtones in the intermittent and rapidly damping
RB signal. The complexity in the dynamics of airflow in BB and RB is investigated
through the fractal dimension, Hurst exponent, phase portrait, maximal
Lyapunov exponent, and sample entropy values. The greater value of entropy
for the RB signal provides an insight into the internal morphology of the airways
containing mucous and other obstructions. The Principal Component Analysis
(PCA) employs PSD features, and Linear Discriminant Analysis (LDA) along
with Pattern Recognition Neural Network (PRNN) uses non-linear measures
for predicting BB and RB. Signal classification based on phase portrait
features evaluates the multidimensional aspects of signal intensities, whereas
that based on PSD features considers mere signal intensities. The principal
components in PCA cover about 86.5% of the overall variance of the data class,
successfully distinguishing BB and RB signals. LDA and PRNN that use nonlinear time-series parameters identify and predict RB and BB signals with 100%
accuracy, sensitivity, specificity, and precision. Novelty: The study divulges the
potential of non-linear measures and PSD features in classifying these signals
enabling its application to be extended for low-cost, non-invasive COVID-19
detection and real-time health monitoring.
Keywords: lung signal, fractal analysis, sample entropy, nonlinear timeseries, machine learning techniques
Published in RUNG: 30.06.2022; Views: 2149; Downloads: 0
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10. Nonlinear time series and principal component analyses: Potential diagnostic tools for COVID-19 auscultationMohanachandran Nair Sindhu Swapna, RAJ VIMAL, RENJINI A, SREEJYOTHI S, SANKARARMAN S, 2020, original scientific article Abstract: The development of novel digital auscultation techniques has become highly significant in the context
of the outburst of the pandemic COVID 19. The present work reports the spectral, nonlinear time series,
fractal, and complexity analysis of vesicular (VB) and bronchial (BB) breath signals. The analysis is carried
out with 37 breath sound signals. The spectral analysis brings out the signatures of VB and BB through
the power spectral density plot and wavelet scalogram. The dynamics of airflow through the respiratory tract during VB and BB are investigated using the nonlinear time series and complexity analyses in
terms of the phase portrait, fractal dimension, Hurst exponent, and sample entropy. The higher degree
of chaoticity in BB relative to VB is unwrapped through the maximal Lyapunov exponent. The principal
component analysis helps in classifying VB and BB sound signals through the feature extraction from the
power spectral density data. The method proposed in the present work is simple, cost-effective, and sensitive, with a far-reaching potential of addressing and diagnosing the current issue of COVID 19 through
lung auscultation.
Keywords: Breath sound analysis, Fractal dimension, Nonlinear time series analysis, Sample entropy, Hurst exponent, Principal component analysis
Published in RUNG: 28.06.2022; Views: 2451; Downloads: 0
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