arXiv subjects

P. Prakash

Publications and source records attributed to P. Prakash.

14 recordsLinked to original sources

arXiv2024

Analytical solutions of higher-dimensional coupled system of nonlinear time-fractional diffusion-convection-wave equations

This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order derivative for the first time. Specifically, we describe how to systematically find different invariant product linear spaces with various dimensions for the considered system. Also, we observe that the obtained invariant product linear spaces help to reduce the multi-component (N+1)-dimensional coupled NTFPDEs into a system of fractional-order ODEs, which can then be solved using the well-known analytical methods. More precisely, we illustrate the effectiveness and importance of this developed method for obtaining a long list of invariant product linear spaces for the multi-component (2+1)-dimensional coupled nonlinear time-fractional diffusion-convection-wave equations. In addition, we have shown how to find different kinds of generalized separable analytical solutions for a multi-component (2 + 1)-dimensional coupled nonlinear time-fractional diffusion-convection-wave equations along with the initial and boundary conditions using invariant product linear spaces obtained. Finally, we provide appropriate graphical representations of some of the derived generalized separable analytical solutions with various fractional-order values.

math.AP↗

arXiv2024

On the solutions of coupled nonlinear time-fractional diffusion-reaction system with time delays

In this article, we systematically explain how to apply the analytical technique called the invariant subspace method to find various types of analytical solutions for a coupled nonlinear time-fractional system of partial differential equations with time delays. Also, the present work explicitly studies a systematic way to obtain various kinds of finite-dimensional invariant vector spaces for the coupled nonlinear time-fractional diffusion-reaction (DR) system with time delays under the two distinct fractional derivatives, namely (a) the Riemann-Liouville fractional partial time derivative and (b) the Caputo fractional partial time derivative. Additionally, we provide details of deriving analytical solutions in the generalized separable form for the initial and boundary value problems (IBVPs) of the coupled nonlinear time-fractional DR system with multiple time delays through the obtained invariant vector spaces under the considered two time-fractional derivatives.

math.AP↗

arXiv2024

Nonlinear two-component system of time-fractional PDEs in (2+1)-dimensions: Invariant subspace method combined with variable transformation

In this article, we develop a systematic approach of the invariant subspace method combined with variable transformation to find the generalized separable exact solutions of the nonlinear two-component system of time-fractional PDEs (TFPDEs) in (2+1)-dimensions for the first time. Also, we explicitly explain how to construct various kinds of finite-dimensional invariant linear product spaces for the given system using the invariant subspace method combined with variable transformation. Additionally, we present how to use the obtained invariant linear product spaces to derive the generalized separable exact solutions of the discussed system. We also note that the discussed method will help to reduce the nonlinear two-component system of TFPDEs in (2+1)-dimensions into the nonlinear two-component system of TFPDEs in (1+1)-dimensions, which again reduces to a system of time-fractional ODEs through the obtained invariant linear product spaces. More specifically, the significance and efficacy of the systematic investigation of the discussed method have been investigated through the initial and boundary value problems of the generalized nonlinear two-component system of time-fractional reaction-diffusion equations (TFRDEs) in (2+1)-dimensions for finding the generalized separable exact solutions, which can be expressed in terms of the exponential, trigonometric, polynomial, Euler-Gamma and Mittag-Leffler functions. Also, 2D and 3D graphical representations of some of the obtained solutions are presented for different values of fractional orders.

nlin.SI↗

arXiv2023

Invariant subspace method for (m + 1)-dimensional non-linear time-fractional partial differential equations

In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method have been systematically investigated through the (3 + 1)-dimensional generalized non-linear time-fractional diffusion-convection-wave equation along with appropriate initial conditions. This systematic investigation provides an important technique to find a large class of various types of the invariant subspaces with different dimensions for the above-mentioned equation. Additionally, we have shown that the obtained invariant subspaces help to derive a variety of exact solutions that can be expressed as the combinations of exponential, trigonometric, polynomial and well-known Mittag-Leffler functions.

nlin.SI↗

arXiv2023

Invariant subspace method to the initial and boundary value problem of the higher dimensional nonlinear time-fractional PDEs

This paper systematically explains how to apply the invariant subspace method using variable transformation for finding the exact solutions of the (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown how to transform the given (k+1)-dimensional nonlinear time-fractional PDEs into (1+1)-dimensional nonlinear time-fractional PDEs using the variable transformation procedure. Also, we explain how to derive the exact solutions for the reduced equations using the invariant subspace method. Additionally, in this careful and systematic study, we will investigate how to find the various types of exact solutions of the (3+1)-dimensional nonlinear time-fractional convection-diffusion-reaction equation along with appropriate initial and boundary conditions for the first time. Moreover, the obtained exact solutions of the equation as mentioned above can be written in terms of polynomial, exponential, trigonometric, hyperbolic, and Mittag-Leffler functions. Finally, the discussed method is extended for the (k+1)-dimensional nonlinear time-fractional PDEs with several linear time delays, and the exact solution of the (3+1)-dimensional nonlinear time-fractional delay convection-diffusion-reaction equation is derived.

nlin.SI↗

arXiv2021

Contact Force Mediated Rapid Deposition of Colloidal Microspheres Flowing Over Microstructured Barriers

Deposition of particles while flowing past constrictions is a ubiquitous phenomenon observed in diverse systems. Some common examples are jamming of salt crystals near the orifice of saltshakers, clogging of filter systems, gridlock in vehicular traffic etc. Our work investigates the deposition events of colloidal microspheres flowing over microstructured barriers in microfluidic devices. The interplay of DLVO, contact and hydrodynamic forces in facilitating rapid deposition of microspheres is discussed. Noticeably, a decrease in the electrostatic repulsion among microspheres leads to linear chain formations, whereas an increase in roughness results in rapid deposition.

cond-mat.soft↗

arXiv2021

Initial value problem for the two-dimensional time-fractional generalized convection-reaction-diffusion-wave equation: Invariant subspaces and exact solutions

This work investigates how we can extend the invariant subspace method to two-dimensional time-fractional non-linear PDEs. More precisely, the systematic study has been provided for constructing the various dimensions of the invariant subspaces for the two-dimensional time-fractional generalized convection-reaction-diffusion-wave equation along with the initial conditions for the first time. Additionally, the special types of the above-mentioned equation are discussed through this method separately such as reaction-diffusion-wave equation, convection-diffusion-wave equation and diffusion-wave equation. Moreover, we explain how to derive variety of exact solutions for the underlying equation along with initial conditions using the obtained invariant subspaces. Finally, we extend this method to two-dimensional time-fractional non-linear PDEs with time delay. Also, the effectiveness and applicability of the method have been illustrated through the two-dimensional time-fractional cubic non-linear convection-reaction-diffusion-wave equation with time delay. In addition, we observe that the obtained exact solutions can be viewed as the combinations of Mittag-Leffler function and polynomial, exponential and trigonometric type functions.

math.AP↗

arXiv2020

Rapid accumulation of colloidal microspheres flowing over microfabricated barriers

Accumulation of particles while flowing past constrictions is a ubiquitous phenomenon observed in diverse systems. Some of the common examples are jamming of salt crystals near the orifice of salt shakers, clogging of filter systems, gridlock in traffics etc. For controlled studies, accumulation events are often examined as clogging process in microfluidic channels. Experimental studies thus far have provided with various physical insights, however, they fail to address commonly encountered accumulation events relevant to human health such as dental and arterial plaques. We simulate arterial plaque like accumulation events by flowing colloidal microspheres over micro-structured barriers in microfluidic environment. Our experiments reveal the role of electrostatic, contact and hydrodynamic forces in facilitating plaque-like build up events. A decrease in Debye length (electrostatic repulsion) between interacting surface by two orders leads to only a minor increase in accumulation. In contrast, an increase in the roughness by 3 times results in dramatic rise of accumulation.

cond-mat.soft↗

arXiv2020

Swimming statistics of cargo-loaded single bacteria

Burgeoning interest in the area of bacteria-powered micro robotic systems prompted us to study the dynamics of cargo transport by single bacteria. In this paper, we have studied the swimming behaviour of oil-droplets attached as a cargo to the cell bodies of single bacteria. The oil-droplet loaded bacteria exhibit super-diffusive motion which is characterized by high degree of directional persistence. Interestingly, bacteria could navigate even when loaded with oil-droplets as large as 8 microns with an effective increase in rotational drag by more than 2 orders when compared to free bacteria. Further, the directional persistence of oil-droplet loaded bacteria was independent of the cargo size.

cond-mat.soft↗

arXiv2020

Exact solutions of generalized non-linear time-fractional reaction-diffusion equations with time delay

In this paper, we propose the invariant subspace approach to find exact solutions of time-fractional partial differential equations (PDEs) with time delay. An algorithmic approach of finding invariant subspaces for the generalized non-linear time-fractional reaction-diffusion equations with time delay is presented. We show that the fractional reaction-diffusion equations with time delay admit several invariant subspaces which further yields several distinct analytical solutions. We also demonstrate how to derive exact solutions for time-fractional PDEs with multiple time delays. Finally, we extend the invariant subspace method to more generalized time-fractional PDEs with non-linear terms involving time delay.

math.AP↗

arXiv2019

Probing the multi spin-phonon coupling and local B-site disorder in Pr2CoFeO6 by Raman spectroscopy and correlation with its electronic structure by X-ray photoemission spectroscopy

Electronic structure near Fermi level of Pr2CoFeO6 (at 300 K) was investigated by X-ray photoemission spectroscopy (XPS) technique. All three cations, i.e., Pr, Co and Fe were found to be trivalent in nature. XPS analysis also suggested the system to be insulating in nature. Moreover, Raman spectroscopy study indicated the random distribution of the B-site ions (Co/Fe) triggered by same charge states. In temperature-dependent Raman study, the relative heights of the two observed phonon modes exhibited anomalous behaviour near magnetic transition temperature TN~270 K, thus indicating towards interplay between spin and phonon in the system. Furthermore, clear anomalous softening was observed below TN which confirmed the existence of strong spin-phonon coupling occurring for at least two phonon modes of the system. The line width analysis of the phonon modes essentially ruled out the role of magnetostriction effect in the observed phonon anomaly. The investigation of the lattice parameter variation across TN (obtained from the temperature-dependent neutron diffraction measurements) further confirmed the existence of the spin-phonon coupling.

cond-mat.str-el↗

arXiv2014

Study of High Temperature Thermal Behavior of Alkyl and Perfluoroalkylsilane Molecules Self-Assembled on Titanium Oxide Nanoparticles

We have studied high temperature thermal behavior of 1H, 1H, 2H, 2H-Perfluorooctyl-trichlorosilane (FOTS) and Octyltrichlorosilane (OTS) molecules self assembled on titanium dioxide (TiO2) nanoparticles using advanced microscopy and spectroscopy technique such as Scanning Electron Microscope (SEM), Dynamic Light Scattering (DLS), X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FTIR). FOTS SAM and OTS SAM coated TiO2 nanoparticles were heated to different temperature range from room temperature (RT) to 550oC. We characterized nano-microstructure and size distribution of FOTS SAM and OTS SAM coated TiO2 nanoparticles, which were heat-treated to different peak temperatures, using SEM and DLS techniques. The thermal stability and degradation of FOTS SAM and OTS SAM coated TiO2 were carried out using FTIR spectroscopy. We found that FOTS SAM on TiO2 is very stable up to 450oC and OTS on TiO2 is stable up to 250oC. Peak frequency, peak intensity and full width half maxima (FWHM) of symmetric and asymmetric CF2 and CH2 confirms our observation. In this study, we successfully synergized the surface and temperature sensitive characteristics of FOTS/OTS SAM and TiO2 nanoparticles in order to use them for highly demanding surface and temperature sensitive nanotechnology applications

cond-mat.mtrl-sci↗

arXiv2014

Design and Development of Surface Modified p and n Type Silicon Sensor for Nitrogen Gas Flow Measurement

We report a gas flow driven voltage generation of Octyltrichlorosilane (OTS) molecules self assembled on silicon wafers (Si wafers). OTS Self assembled Monolayer (SAM) has been coated on both p-type and n-type doped silicon wafers (p-Si and n-Si wafers) using dip coating method. We have measured the flow induced voltage generation on OTS SAM coated Si wafers/ Uncoated Si wafers at modest gas flow velocities of subsonic regime (Mach number < 0.2) using national instruments NI-PXI-1044 Workstation. The gas flow driven voltage generation is mainly due to the interplay mechanisms of Bernoulli principle and Seebeck effect. The surface morphology of OTS SAM coated p-Si and n-Si wafers were characterized by SEM analysis. In this study, our results shows that OTS SAM coated p-Si and n-Si wafers shows better sensitivity towards nitrogen gas flow when compared with the uncoated Si wafers. OTS SAM also exhibits high thermal stability and hydrophobicity.

physics.ins-det↗

arXiv2013

What is the difference? Blazhko and non-Blazhko RRab stars and the special case of V123 in M3

In an extended photometric campaign of RR Lyrae variables of the globular cluster M3, an aberrant light-curve, non-Blazhko RRab star, V123, was detected. Based on its brightness, colors and radial velocity curve, V123 is a bona fide member of M3. The light curve of V123 exhibits neither a bump preceding light minimum, nor a hump on the rising branch, and has a longer than normal rise time, with a convex shape. Similar shape characterizes the mean light curves of some large-modulation-amplitude Blazhko stars, but none of the regular RRab variables with similar pulsation periods. This peculiar object thus mimics Blazhko variables without showing any evidence of periodic amplitude and/or phase modulation. We cannot find any fully convincing answer to the peculiar behavior of V123, however, the phenomenon raises again the possibility that rotation and aspect angle might play a role in the explanation of the Blazhko phenomenon, and some source of inhomogeneity acts (magnetic field, chemical inhomogeneity) that deforms the radial pulsation of Blazhko stars during the modulation.

astro-ph.SR↗