The linear and nonlinear motions of a damped rigid planar pendulum, driven by vibrating its pivot sinusoidally, are reexamined. The pendulum is known to exhibit periodic, quasiperiodic, and chaotic motions. Floquet analysis identifies regions of instability and stability within the driving parameter space. A new type of nonlinear oscillation may occur at driving parameters where Floquet analysis predicts a stable stationary state. Such non-Floquet oscillations always have periods longer than twice the period of the vibrating pivot. The possible periods of these oscillations may be four, six, eight, or twelve times the driving period. The power spectrum of the pendulum's angular velocity during these oscillations reveals a novel feature: the two dominant response frequencies sum to the driving frequency.

While the first part1 of the article presented analytic results for a driven coplanar double pendulum with velocity-dependent damping, this second part presents a simple method to compute Floquet multipliers numerically. Multiple regions of harmonic and subharmonic swings in the plane of driving parameters are constructed using the computed values of the Floquet multipliers. The instability zones corresponding to two normal modes may overlap in the plane of driving parameters. The double pendulum cannot oscillate in one of its normal modes within these overlapping regions. The instability zones of the driven damped double pendulum reveal novel features when the two masses are unequal. Two overlapping subharmonic (or harmonic) instability zones detach from their meeting point and shift upwards or sideways in the parameter plane in the presence of damping. The reorganisation of instability zones significantly influences the dynamics.

- We present the nonlinear motions of a partially inverted coplanar double pendulum with velocity-dependent damping under parametric driving. It shows a new type of complex periodic and quasiperiodic oscillations where the sum of two dominating frequencies of the solution is equal to the driving frequency, which is analogous to the phenomenon of spontaneous parametric down-conversion (SPDC). The dominating response frequencies of the double pendulum are independent of the normal mode frequencies when such motion occurs.

This article discusses the preparation of different grades of single-ion conducting quasi-solid polymer electrolytes (q-SPE) material (Chit-g-SPA-IL) based on biopolymer (chitosan), polyacrylic acid and DBU-acetate (DBUH+ AcO-) ionic liquid. Chit-SPA-60 %-IL exhibited the highest conductivity within the range of 10(-4) S/cm. TGA analysis demonstrated the stability of electrolytes up to a temperature of 120 degrees C. SEM-EDS analysis unveiled the porous nature of the electrolyte and even distribution of ions throughout the matrix. It exhibited an electrochemical stability window (EWS) of 2.53 V with significant current density and an ionic transference number (ITN) of similar to 99.9 %. The temperature-dependent conductivity established an Arrhenius-type conduction mechanism with an activation energy of 0.149 eV for ion movement within the electrolyte matrix. The AC conductivity analysis emphasized the time-temperature independence of the ionic conduction mechanism. Dielectric analysis highlighted the capacitive nature of the electrolyte, underlining its substantial capacitance, while modulus studies indicated minimal influence from the electrode-electrolyte interface. Chit-SPA-60 %-IL at 30 degrees C included a self-diffusion coefficient of 4.57 x 10(-5) m(2)/s, ionic mobility of 1.75 x 10(-3) m(2)/Vs, and drift ionic velocity of 0.44 m/s. These findings makes SPE as a promising candidate for sodium-ion-based energy storage devices.

We present the results of linear stability of a damped coplanar double pendulum and its nonlinear motion, when the point of suspension is vibrated sinusoidally in the vertical direction with amplitude a and frequency ω. A double pendulum has two pairs of Floquet multipliers, which have been calculated for various driving parameters. We have considered the stability of a double pendulum when it is in any of its possible stationary states: (i) both pendulums are either vertically downward or upward and (ii) one pendulum is downward and other is upward. The damping is considered to be velocity-dependent, and the driving frequency is taken in a wide range. A double pendulum excited from its stable state shows both periodic and chaotic motion. The periodic motion about its pivot may be either oscillatory or rotational. The periodic swings of a driven double pendulum may be either harmonic or subharmonic for lower values of a. The limit cycles corresponding to the normal mode oscillations of a double pendulum of two equal masses are squeezed into a line in its configuration space. For unequal masses, the pendulum shows multi-period swings for smaller values of a and damping, while chaotic swings or rotational motion at relatively higher values of a. The parametric driving may lead to stabilization of a partially or fully inverted double pendulum.

In the past years, the generalized maximum correntropy criterion (GMCC) has been widely used in adaptive filters to provide robust behavior under non-Gaussian/impulsive noise environments. However, GMCC-based adaptive filters are affected by high steady-state misalignment. In order to enhance the robustness under non-Gaussian noise environments and reduce steady-state misalignment, a generalized modified Blake–Zisserman (GMBZ) robust loss function is introduced in this correspondence. Furthermore, a GMBZ adaptive filter (GMBZ-AF) has been developed that provides improved convergence performance over other existing algorithms. The proposed learning scheme has a computational complexity very similar to that of the GMCC-based adaptive filtering method. In order to further exploit the sparse nature of the system for identifying sparse systems and simultaneously provide robust convergence, two new robust sparse adaptive filters: 1) zero attracting GMBZ-AF (ZA-GMBZ-AF) and 2) reweighted ZA-GMBZ-AF (RZA-GMBZ-AF) have also been proposed. To further enhance the filter convergence performance, a new robust and sparsity-aware loss function called generalized modified dual Blake–Zisserman (GMDBZ) is also introduced in this correspondence and the corresponding GMDBZ adaptive filter (GMDBZ-AF) has been developed.

Dynamic behavior of armor steel grade has been investigated by implementing Johnson-Cook plasticity and failure models. The stress and strain curves obtained from the experiments at different strain rates (10−4-1550 s−1) and temperatures (25-600 °C) were used to calibrate the parameters of Johnson-Cook plasticity model. Parameters of Johnson-Cook failure model were obtained by combining finite element modeling with tensile tests. Validation of Johnson-Cook material parameters is performed using finite element simulations and digital image correlation experiments performed on notch specimens of radii between 2 and 6 mm under uniaxial tension. The ballistic impact tests were performed on 6 mm thick armor plate against 7.62 × 39 mm hardened steel core and 7.62 × 54 mm armor-piercing projectiles. The armor plate when impacted against 7.62 × 39 mm projectile exhibits indentation, while the plate undergoes complete penetration when impacted against 7.62 × 54 mm projectile. Results of ballistic tests at different incident velocities were compared by carrying out numerical simulations on armor steel plate. The ballistic limit of the plate, when impacted against 7.62 × 54 mm projectile, is obtained from numerical simulation and estimated as 825 m/s. The plate experiences a high strain rate and hence a temperature rise during the impact. The present work investigates the increase in temperature in the plate during the ballistic impact at different incident velocities. The temperature of the plate was estimated to increase up to half of its melting temperature, 810-952 K, when impacted against the 7.62 × 54 mm projectile at varying velocities between 820 and 950 m/s.

Chronic diseases are the most severe health concern today, and heart disease is one of them. Coronary artery disease (CAD) affects blood flow to the heart, and it is the most common type of heart disease which causes a heart attack. High blood pressure, high cholesterol, and smoking significantly increase the risk of heart disease. To estimate the risk of heart disease is a complex process because it depends on various input parameters. The linear and analytical models failed due to their assumptions and limited dataset. The existing studies have used medical data for classification purposes, which help to identify the exact condition of the patient, but no one has developed any correlation equation which can be directly used to identify the patients. In this paper, mathematical models have been developed using the medical database of patients suffering from heart disease. Curve fitting and artificial neural network (ANN) have been applied to model the condition of patients to find out whether the patient is suffering from heart disease or not. The developed curve fitting model can identify the cardiac patient with accuracy, having a coefficient of determination (R 2-value) of 0.6337 and mean absolute error (MAE) of 0.293 at a root mean square error (RMSE) of 0.3688, and the ANN-based model can identify the cardiac patient with accuracy having a coefficient of determination (R 2-value) of 0.8491 and MAE of 0.20 at RMSE of 0.267, it has been found that ANN provides superior mathematical modeling than curve fitting method in identifying the heart disease patients. Medical professionals can utilize this model to identify heart patients without any angiography or computed tomography angiography test.

We present results of direct numerical simulations on anisotropy in the velocity and the convective temperature fields of turbulent Rayleigh–Bénard convection in low-Prandtl-number fluids with and without uniform rotation about the vertical direction. Our results are in the intermediate range of Rayleigh number (Ra∼106−108) and high Rossby number (Ro>1). The probability distribution for the fluctuating velocity field v shows exponential tails. The distribution function for the vertical velocity is significantly different from those for the horizontal velocity components, which we take as a mark of anisotropy. The probability distribution function for the fluctuating temperature field θ is also quite different from that of any component of the velocity field and is proportional to exp [−(θ/θ0)4], where θ0 is a constant. To study the anisotropy in Fourier space, we look at the Fourier modes of the velocity fields and compare our numerical results with a calculation based on an effective linear model.

The recently proposed affine projection Versoria (APV) algorithm has been widely used over other affine based algorithms due to its robustness against impulsive noises. However, the performance of the APV algorithm suffers from high steady state misalignment. In order to overcome this, we propose affine projection Champernowne adaptive filter (APCMAF) in which instead of taking Versoria function as a cost function we have used the probability density function of the Champernowne distribution as a cost function and data reuse technique. The proposed APCMAF algorithm provides low steady-state misalignment in impulsive noise environment. To verify the performance of the APCMAF algorithm, a set of simulation study has been done in system identification scenarios which confirms that the APCMAF provides better steady state performance with improved convergence performance over other existing algorithms in impulsive noise environments. Further, the bound of learning rate for stable convergence has been also derived and a detailed comparison of computational complexity is also presented.

Two low-dimensional models for nonlinear dynamo action in Rayleigh-Benard convection in presence of rigid body rotation about vertical axis are constructed for metallic fluids with finite magnetic Prandtl number (Pm) and small (or zero) thermal Prandtl number (Pr). Dynamo effect is seen for Pm >= 0.75 with Pr = 0.025 and Taylor number, 0 < Ta <= 1000. The value of reduced Rayleigh number at the dynamo onset (r(d)) varies with Pm, P rand Ta. The value of r(d) decreases with increase in Pm and Ta separately, if the other two parameters are kept fixed to some small values. However r(d) increases slightly if Pr is increased, the value being minimum for Pr = 0. When 0.75 <= Pm < 4, dynamo onset appears as intermittent chaotic burst. The intermittent burst changes to continuous chaos with rise in Pm. The probability mass of the height of peak in average magnetic energy follows power law when Pm is small. For 4 <= Pm < 6 and 600 <= Ta < 1000 dynamo effect starts at the onset of convection as finite oscillation. This effect continues in a small window of rand then disappears. The dynamo action again appears as quasi-periodic wave or chaotic wave for further increase in r. (C) 2020 Elsevier Ltd. All rights reserved.

We present the results of direct numerical simulations of power spectral densities for kinetic energy, convective entropy, and heat flux for unsteady Rayleigh–Bénard magnetoconvection in the frequency space. For larger values of frequency, the power spectral densities for all the global quantities vary with frequency (f) as f−2. The scaling exponent is independent of Rayleigh number, Chandrasekhar’s number, and thermal Prandtl number.

In recent years, correntropy-based algorithms which include maximum correntropy criterion (MCC), generalized MCC (GMCC), kernel MCC (KMCC) and hyperbolic cosine function-based algorithms such as hyperbolic cosine adaptive filter (HCAF), logarithmic HCAF (LHCAF), least lncosh (Llncosh) have been widely utilized in adaptive filtering due to their robustness towards non-Gaussian/impulsive background noises. However, the performance of such algorithms suffers from high steady-state misalignment. To minimize the steady-state misalignment along with having comparable computational complexity, an exponential hyperbolic cosine function (EHCF) based new robust norm is introduced and a corresponding EHCF based adaptive filter called exponential hyperbolic cosine adaptive filter (EHCAF) is developed in this letter. Further, computational complexity and bound on learning rate for stability of the proposed algorithm is also studied. A set of simulation studies has been carried out for system identification scenario to assess the performance of the proposed algorithm. Further, EHCAF algorithm has been extended and the filtered-x EHCAF (Fx-EHCAF) algorithm is proposed for robust room equalization.

We present dynamic models of dynamo action in the low-Prandtl-number ( Pr≤0.1 ) regime which highlight the role of pure thermal convection in magnetic field generation. The essential condition for dynamo to occur is non-zero values of the magnetic Prandtl number Pm. Magnetic energy is generated in conducting fluids close to the convective instability if the reduced Rayleigh number r is raised above a critical value r d , otherwise only pure convection is prevalent. The dynamo threshold decreases with increase in Pm for a fixed value of Pr while for a fixed Pm, it increases with increase in Pr. For a fixed Pr, the induced magnetic energy is excited in the form of irregular bursts for lower values of Pm. The magnetic energy is found to be quasi-periodic or oscillatory for relatively larger values of Pm. The bursts of magnetic energy also show the possibility of flow reversals. In the chaotic regime, the probability density function of the heights of magnetic energy bursts show scaling behavior. The results are relevant for magnetic field generation induced by astrophysical plasma flows in localized convection zones of solar/stellar interiors where Pr is very low and Pm≤10 .

Here, a bifunctional quinine-derived benzamide catalyzed direct enantioselective vinylogous aldol reaction between 3-alkylidene-2-oxindoles and pyrazole-4,5-diones has been developed.

We present the results of an experimental investigation on parametrically driven waves in a water half-cylinder on a rigid horizontal plate, which is sinusoidally vibrated in the vertical direction. As the forcing amplitude is raised above a critical value, stationary waves are excited in the water half-cylinder. Parametrically excited subharmonic waves are non-axisymmetric and qualitatively different from the axisymmetric Savart–Plateau–Rayleigh waves in a vertical liquid cylinder or jet. Depending on the driving frequency, stationary waves of different azimuthal wave numbers are excited. A linear theory is also supplemented, which captures the observed dispersion relations quantitatively.

A silver tetrafluoroborate catalyzed domino cycloisomerization-vinylogous aldol addition sequence on a multifunctional substrate such as ortho-alkynylbenzaldehydes yielding functionalized 1H-isochromenes in a single step with high yield and excellent diastereoselectivity (>19 : 1) is described. The reaction was well tolerated by alkyl, aryl, and unsubstituted alkynylbenzaldehydes, and furnished selective 6-endo-dig adducts exclusively without loss in the regio- as well as diastereoselectivity.

Floquet analysis of modulated magnetoconvection in Rayleigh–Bénard geometry is performed. A sinusoidally varying temperature is imposed on the lower plate. As Rayleigh number Ra is increased above a critical value Ra o , the oscillatory magnetoconvection begins. The flow at the onset of magnetoconvection may oscillate either subhar- monically or harmonically with the external modulation. The critical Rayleigh number Ra o varies non-monotonically with the modulation frequency ω for appreciable value of the modulation amplitude a . The temperature modulation may either postpone or prepone the appearance of magnetoconvection. The magnetoconvective flow always oscillates harmonically at larger values of ω . The threshold Ra o and the corresponding wavenumber k o approach to their values for the stationary magnetoconvection in the absence of modulation ( a = 0), as ω → ∞. Two different zones of harmonic instability merge to form a single instability zone with two local minima for higher values of Chandrasekhar’s number Q , which is qualitatively new. We have also observed a new type of bicritical point, which involves two different sets of harmonic oscillations. The effects of variation of Q and Pr on the threshold Ra o and critical wavenumber k o are also investigated.

High strength steel plates are majorly utilized for civil and military vehicles for ballistic protection against various threat levels. In this work, an experimental and numerical study has been conducted on a newly developed armour steel grade. Four different ductile fracture criteria have been used in the numerical simulations, namely Modified Johnson-Cook (MJC), Cockcroft-Latham (CL), Constant failure strain (CFS) and Maximum Shear (MS) stress failure criteria. Suitable experiments were conducted for material model parameter estimation and a simulation study was conducted in LS-DYNA to evaluate its performance in a plate impact simulation. The results were correlated with an actual Impact test done with a plate of dimension 1000 x 1000 x 6 mm with 7.62 x 51 mm NATO ball ammunition for NIJ (National Institute of Justice) Level 3 protection. Modified Johnson-Cook, Cockcroft-Latham and Constant strain failure criteria are in good agreement with experimental results. Maximum Shear stress failure criteria failed to predict the experimental results.

Understanding of material behavior of armour steel under large deformations and high strains during loading is very crucial in designing steel structures for various applications. Johnson–Cook flow stress and Johnson–Cook failure models were adopted for modeling and predicting the material flow behavior of armour plate. The material parameters of Johnson–Cook flow stress have been determined experimentally from tests performed at different strain rates (10−4–1550 s−1) and temperatures (25–600 °C). The damage parameters of Johnson–Cook failure model were determined through experiments on flat tensile specimens in combination with finite element simulation. Using these materials parameters, finite element simulations were performed on notch specimens of different radii between 2 mm and 20 mm loaded under tension. Load-strain curves were in good agreement with the experimentally obtained data. Triaxiality obtained from simulation were matched against the reported values from the literature.