Eigenvalue Approach Research Articles

Eigenvalue method for the solution of multi-compartment model of HIV-AIDS transmission

The aim of this study is to formulate a multi-compartment mathematical model regarding the transmission and dynamics of HIV-AIDS. The model is formulated on the basis of a system of linear, ordinary differential equations and admits two locally and globally stable equilib-ria. Primarily, the existence and uniqueness of solution of the model are demonstrated which is then obtained analytically using the fundamental matrix method and eigenvalue approach. The obtained solution serves as the pedestal for studying the dynamics and spread of HIV-AIDS in gen-eral. Nevertheless, as an endorsement to the obtained results the simu-lations are also carried out with model outcomes being contrasted to the exact data of the disease in India.

Far-Field Correlations Verifying Non-Hermitian Degeneracy of Optical Modes.

An experimental verification of an exceptional point (EP) in a stand-alone chaotic microcavity is a tough issue because as deformation parameters are fixed the traditional frequency analysis methods cannot be applied any more. Through numerical investigations with an asymmetric Reuleaux triangle microcavity (ARTM), we find that the eigenvalue difference of paired modes can approach near-zero regardless of nonorthogonality of the modes. In this case, for a definite verification of EPs in experiments, wave function coalescence should be confirmed. For this, we suggest the method of exploiting correlation of far-field patterns (FFPs), which is directly related to spatial mode patterns. In an ARTM, we demonstrate that the FFP correlation of paired modes can be used to confirm wave function coalescence when an eigenvalue difference approaches near zero.

Linear Temporal Stability Analysis of Dual Solutions for a Ti-Alloy Nanofluid with Inclined MHD and Joule Effects: Flow Separation

The impacts of tilted magnetic field and Joule heating on a Ti-alloy nanofluid towards an exponentially permeable stretching/shrinking surface have been looked into in this article. The Tiwari and Das model is adopted for the nanofluid where water is taken as the base fluid and Ti-alloy as the nanoparticles. The dual solutions of the resultant non-dimensional flow equations are evaluated using Shooting and 4th order Runge-Kutta methods and then linear temporal stability analysis is conducted to verify its stability through the smallest eigenvalue approach. The graphical representation of the results for the Ti-alloy/water nanofluid is presented to illustrate interesting features and its stability in the presence of physically effective parameters like inclined magnetic, Joule, volume fraction, and suction parameters. Outcomes of the numerical findings indicate that the dual/multiple solutions are possible only within the limited range of inclined magnetic and suction parameters. Through eigenvalue patterns, it is noticed that the 1st solution is realistic and stable while the 2nd solution is unreliable for each combination. In addition, the streamlines are also displayed to visualize the flow patterns of the Ti-alloy nanofluid. Also, the flow separation point is found in between the shrinking and stretching regions. Finally, the delay of boundary layer separation is pointed out with the enhancing values of volume fraction of Ti-alloy nanoparticles and magnetic parameter in the presence of suction. This kind of analysis performs a very crucial role in the medical sector, aerodynamics and space sciences.

An approach for assessing the effects of porous materials on controlling the tire cavity resonance noise

Pasting porous material on the inner surface of a tire is an effective means to mitigate the tire cavity resonance noise. However, its performance is highly related to the material properties and geometry. This paper proposes an eigenvalue analysis approach based on the multi-domain boundary element method (MBEM) to evaluate this performance and further help determine the optimal parameters of the porous material lining in a tire. In this approach, the porous material is equivalent to a fluid, and the MBEM is used to model the sound fields in the air and equivalent fluid domains inside the tire cavity, based on which the eigenvalue analysis is conducted and the associated nonlinear eigenproblem is solved by using a contour integral method. The accuracy and validity of the proposed method are first verified by using a two-dimensional tire model with analytical solution, and then testified by comparing with the experimental results of a real tire lined with porous materials with different flow resistivities, thicknesses and widths. Furthermore, the effects of porous materials with different parameters are investigated based on the proposed method and the optimal parameters are suggested for a typical three-dimensional tire model.

Post-buckling and vibration analysis of randomly distributed CNT reinforced fibre composite plates under localised heating

Present study aims to investigate the non-linear stability and vibration characteristics of randomly distributed carbon nanotube reinforced fiber composites (RD-CNTRFC) under localized heating. The effective material properties of RD-CNT reinforced polymer is determined using Eshelbhy-Mori-Tanaka (EMT) approach and Chamis method is used to estimate the material properties of the RD-CNTRFC plates considering properties to be temperature-dependent. The strain-displacement fields of plates are developed using Reddy’s higher order shear deformation theory and von-Kármán non-linearities. The in-plane pre-buckling stresses within the plates due to localized heating are estimated using Airy’s stress function by satisfying compatibility equation. Galerkin’s approach is adopted to simplify the partial differential equations (PDEs) into non-linear algebraic equations for stability analysis and ordinary differential equations (ODEs) for vibration analysis. The critical temperature of the plates can be obtained using standard eigen value approach and thermal non-linear equilibrium path of plate can be traced using iterative eigen value approach. The present approach is initially verified with the results of published literature. Moreover various parametric studies like agglomeration effect of CNTs, mass fraction of CNT, aspect ratio, width-to-thickness ratio are also carried-out to elucidate their influence on thermal stability and vibration characteristics of RD-CNTRFC plates.

Algebraic solution of the Hartree equation based on a tensor eigenvalue approach

Algebraic solution of the Hartree equation based on a tensor eigenvalue approach

Moore-Gibson-Thompson theory of a non-local excited semiconductor medium with stability studies

The present study introduces a theoretical framework according to the Moore-Gibson-Thompson (MGT) Model in the context of generalized thermoelasticity theory. The excited semiconductor material is utilized to formulate the governing equations in one dimensional (1D) with a non-local parameter. According to the photo- thermoelasticity theory, the overlapping between the electronic (optical) deformation and elastic deformation is taken into account. During the photo-excitation processes, the non-local equation of motion and the heat equation is introduced according to the model of Moore-Gibson-Thompson (MGT). The novel model describes the interaction between plasma and thermomechanical waves in a non-dimensional form. Laplace transform for time variable is applied to convert the governing equations into system of ordinary differential equations. The vector-matrix differential equation with the eigenvalues approach method is employed to obtain the solutions of the physical quantities analytically. Laplace transform invers numerically is utilized when some boundary conditions are applied at the semiconductor free surface to obtain the complete general of the main physical quantities. The numerical computations for the input parameters of Silicon as semiconductor material are used to illustrate the obtained results graphically and discussed.

Dual solutions and their stability analysis for inclined magnetohydrodynamics and Joule effects in Ti-alloy nanofluid: Flow separation

This article emphasizes the roles of Joule heating and inclined magnetic field on the Ti-alloy nanofluid towards an exponentially permeable shrinking/stretching surface for the first time. Adopting the Tiwari and Das model, this nanofluid incorporates water as the base fluid and Ti-alloy as the nanoparticles in the mathematical formulation. Non-dimensional form of resultant flow governing equations is solved numerically for dual solutions using the Shooting method along with the Runge-Kutta fourth order technique and also the stability of the system is verified through the eigenvalue approach. The streamlines and eigenvalue patterns are provided to show the stability of obtained solutions and the significance of the problem undertaken. In these solutions, the first solution is found to be realistic and stable whereas the second solution is not stable for each combination of inclined magnetic, Joule heating, stretching/shrinking, Ti-alloy volume fraction, and suction parameters within the limited ranges. The existence of a flow separation point is identified between the shrinking and stretching regions. Finally, the delay of boundary layer separation is pointed out with the enhancing values of volume fraction of Ti-alloy nanoparticles and magnetic parameter in the presence of suction. This kind of analysis plays a very important role in the fields of aerodynamics, medical, and space sciences.

Memory Response on the Elasto-Thermodiffusive Interaction Subjected to Harmonically Varying Heat Source

Enlightened by the Caputo type of fractional derivative, this research paper is the analysis of a mathematical model of generalized thermoelastic diffusion with memory-dependent derivative (MDD) for an isotropic infinite medium with a cylindrical cavity in the context of dual-phase lag model. The surface of the cavity is traction free and subjected to harmonically heat sources with constant angular frequency of thermal vibration. Laplace transform technique has been used to solve the problem. Later eigenvalue approach is used to obtain the analytical expressions for different physical fields in the transformed domain. Finally to obtain the solutions in the real-time domain, the Riemann-sum approximation method is used. According to the graphical representations corresponding to the numerical results, the effect of heat source speed on temperature, displacement, stress, mass concentration and chemical potential are studied. The effect of memory-dependent parameters, as well as in the absence of MDD on physical quantities are also demonstrated.

Eigenvalue approach to study Rayleigh waves in nonlocal orthotropic layer lying over nonlocal orthotropic half-space with dual-phase-lag model

In this present article, we deal with the propagation of Rayleigh surface waves in the nonlocal orthotropic thermoelastic layer which is lying over a nonlocal orthotropic thermoelastic half-space in the context of the dual-phase-lag model. This problem is considered in the context of Eringen’s nonlocal elasticity theory. A vector-matrix differential equation is obtained which is solved by an eigenvalue approach. The frequency equation of Rayleigh surface waves is derived and various particular cases are discussed. The different characteristics namely attenuation coefficient, specific loss, penetration depth, and phase velocity are presented graphically with respect to frequency.

An eigenvalue ratio approach to inferring population structure from whole genome sequencing data.

Inference of population structure from genetic data plays an important role in population and medical genetics studies. With the advancement and decreasing cost of sequencing technology, the increasingly available whole genome sequencing data provide much richer information about the underlying population structure. The traditional method originally developed for array-based genotype data for computing and selecting top principal components (PCs) that capture population structure may not perform well on sequencing data for two reasons. First, the number of genetic variants p is much larger than the sample size n in sequencing data such that the sample-to-marker ratio is nearly zero, violating the assumption of the Tracy-Widom test used in their method. Second, their method might not be able to handle the linkage disequilibrium well in sequencing data. To resolve those two practical issues, we propose a new method called ERStruct to determine the number of top informative PCs based on sequencing data. More specifically, we propose to use the ratio of consecutive eigenvalues as a more robust test statistic, and then we approximate its null distribution using modern random matrix theory. Both simulation studies and applications to two public data sets from the HapMap 3 and the 1000 Genomes Projects demonstrate the empirical performance of our ERStructmethod.

Performance of fast responding ultracapacitor energy storage for virtual inertia emulation control

AbstractThis paper proposes a black widow optimization (BWO) algorithm‐based derivative‐type control for optimized virtual inertia (VI) emulation using fast responding ultracapacitor (UC) as energy storage system for frequency regulation in a two‐area deregulated power system composed of thermal and hydro units with high penetration of solar photovoltaic. The parameters of the system have been controlled by using newly formulated BWO and their performance have been compared for virtual inertial emulation efficacy with other algorithms under different contract obligations. The impact of the coordinated action of BWO‐based proportional‐integral (PI) controller with VI emulation has been validated on the area frequency, tie‐line power, and generated power of different units. The eigenvalue approach has been applied to verify the performance and effect of VI emulation control using fast acting UC on system stability. The proposed VI emulation control studies have been evaluated under nonlinear environment of deregulated power system. The comparative studies show that BWO optimized PI‐based VI emulation using fast responding UC provides superior dynamic responsiveness in all competitive electricity market scenarios tested under different operating conditions.

Minimum-energy synchronization for interconnected networks with non-periodical information silence

Minimum-energy synchronization control for interconnected networks is addressed, where network topologies contain leaderless and leader-follower structures and information transmission of the whole network is non-periodically silent. The key characteristic of the current work is that the total energy consumption is minimum in the sense of the linear matrix inequality, while both the guaranteed-cost synchronization and the limited-budget synchronization cannot make the total energy consumption be minimum. Firstly, the leaderless minimum-energy synchronization achievement problem is transformed into the asymptotic stabilization problem by the state decoupling strategy, and sufficient conditions of leaderless minimum-energy synchronization are presented by the Lyapunov-based method. Especially, those conditions can be solved by the generalized eigenvalue approach on the basis of the linear matrix inequality. Then, main results of leaderless minimum-energy synchronization are expanded to leader-follower interconnected networks, where the key challenge is that these networks are nonsymmetrical. Finally, two numerical examples are illustrated to verify main results.

Eigenvalues approach on thermo-elastic diffusions problem for an infinite material containing spherical holes

In this article, the thermoelastic diffusion interaction in an unbounded medium containing spherical holes in the context Green-Naghdi model of type III are studied. The inner surface of hole is taken to be tractions free and due to an exponent of the decayed heat flux. The Laplace transforms techniques are used. The eigenvalues approaches are adopted for the solutions of applications for infinite media with a spherical hole. The numerical results for the concentration, the displacement, the chemical potential, the temperature, and the stress are presented analytical and graphically.

Effects of the Nonlocal Thermoelastic Model in a Thermoelastic Nanoscale Material

In this work, a novel nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach. The basic equations are applied under the Green and Naghdi model without energy dissipations. To obtain this model, the theory of the non-local continuum suggested by Eringen is applied. The Laplace transformation technique is used for the basic formulations to obtain the analytical solutions of the thermal stress, the displacement, and the temperature during the nanoscale thermo-electric medium. The inverse of the Laplace transformation is used with the numerical technique to obtain the complete solutions of the studying fields in the time–space domains. The main physical fields are displayed graphically and theoretically discussed under the influence of nonlocal parameters.

Hall current effect in double poro-thermoelastic material with fractional-order Moore–Gibson–Thompson heat equation subjected to Eringen's nonlocal theory

The present study focuses on the analysis of one-dimensional thermoelastic interaction in an infinite medium consisting of double poro-thermoelastic material with voids (DPTMWV) in the presence of Hall current by developing the fundamental relations in light of Eringen's nonlocal elasticity theory. A fractional-order Moore–Gibson–Thompson (MGT) heat conduction equation is introduced to the model in the context of a continuous heat source. The Caputo fractional derivative is applied in the domain of Laplace transform. The displacement, temperature, volume fractions, and stresses are determined with the help of the eigenvalue approach and the numerical inversions of these physical variables are obtained by using Zakian's algorithm. The effects of several parameters, such as Hall current, fractional order, nonlocality, and time, are graphically executed. Furthermore, the nonlocal models under different generalized thermoelasticity theories are compared to visualize the variations in the distributions corresponding to the prior mentioned variables.

Holographic insulator/superconductor phase transition via matching method and thermodynamic geometry approach

This paper employs two analytical techniques, namely, the matching method and the thermodynamic geometry approach to investigate the insulator/superconductor phase transition holographically in the presence of a five-dimensional AdS soliton background. This is a sequel of our earlier work [D. Parai, S. Gangopadhyay and D. Ghorai, Ann. Phys. 403, 59 (2019)] where we carried out a similar analysis using the Sturm–Liouville eigenvalue approach. We have first used the matching method to obtain the critical chemical potential, condensation operator and the charge density. Next, we investigate the free energy and thermodynamic geometry of this model. This investigation of the thermodynamic geometry leads to the critical chemical potential of the system from the condition of the divergence of the scalar curvature. We have then compared the value of the critical chemical potential [Formula: see text] obtained from these two different methods. The findings are then compared with the numerical and analytical results obtained from the Sturm–Liouville technique.

The Influences of the Hyperbolic Two-Temperatures Theory on Waves Propagation in a Semiconductor Material Containing Spherical Cavity

This article focuses on the study of redial displacement, the carrier density, the conductive and thermodynamic temperatures and the stresses in a semiconductor medium with a spherical hole. This study deals with photo-thermoelastic interactions in a semiconductor material containing a spherical cavity. The new hyperbolic theory of two temperatures with one-time delay is used. The internal surface of the cavity is constrained and the density of carriers is photogenerated by a heat flux at the exponentially decreasing pulse boundaries. The analytical solutions by the eigenvalues approach under the Laplace transformation approaches are used to obtain the solution of the problem and the inversion of the Laplace transformations is performed numerically. Numerical results for semiconductor materials are presented graphically and discussed to show the variations of physical quantities under the present model.

Eigenvalue fusion-based machine learning approach for cooperative spectrum sensing in cognitive radio

Spectrum sensing is the most critical and fundamental function of the cognitive radio (CR) for dynamic spectrum usage. Machine learning (ML) techniques that allow CRs to learn the environment adaptively are most essential in spectrum sensing. This paper proposes a novel machine learning-based cooperative spectrum sensing (CSS) technique using various advanced ML schemes to enhance the probability of detection. ML classifiers used in the fusion centre of the CSS schemes are trained with eigenvalue-based test statistics extracted from the covariance matrix of a received signal. The proposed system recognises the received signal samples as a PU signal or a noise signal and distinguishes the PU signal from noise effectively under low SNR conditions using a threshold that possesses the self-learning ability. The simulation results exhibit the performance analysis of various ML algorithms for CSS under different wireless scenarios and their suitability is compared with conventional approaches.

Novel vortices and the role of a complex chemical potential in a rotating holographic superfluid

In this work, we have analytically devised novel vortex solutions in a rotating holographic superfluid. To achieve this result, we have considered a static disc at the AdS boundary and let the superfluid rotate relative to it. This idea has been numerically exploited in [1] where formation of vortices in such a setting was reported. We have found that these vortex solutions are eigenfunctions of angular momentum. We have also shown that vortices with higher winding numbers are associated with higher quantized rotation of the superfluid. We have, then, analysed the equation of motion along bulk AdS direction using St\"urm-Liouville eigenvalue approach. A surprising outcome of our study is that the chemical potential must be purely imaginary. We have then observed that the winding number of the vortices decreases with the increase in the imaginary chemical potential. We conclude from this that imaginary chemical potential leads to less dissipation in such holographic superfluids.