Browsing by Author "Bhattacharya, Sukalyan (TTU)"
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Item Natural frequencies of a bubble near a solid sphere(2022) Liu, Bo (TTU); Bhattacharya, Sukalyan (TTU)This paper presents an analytical and computational method to describe natural frequencies of a spherical bubble residing near a solid sphere of an arbitrary size in an otherwise unbounded fluid. Under low capillary and Reynolds number limits, the relevant hydrodynamic fields are converted into time-invariant but frequency-dependent quantities by temporal Fourier transform. Then, the spatial variations in the velocity and the pressure can be expressed in terms of two sets of harmonic basis functions involving spherical coordinates centered around the particle and the bubble. A subsequent derivation of transformation coefficients between the aforementioned two sets allows a matrix equation relating the unknown amplitudes to the boundary conditions at all interfaces. Finally, natural frequencies corresponding to different modes of pulsation are obtained from the eigenvalues of the constructed matrix. The results show fast convergence of the computed frequencies with the increasing number of basis functions. These values change significantly with the distance of the bubble from the particle and even decay to zero for some modes when their surface-to-surface separation vanishes. Furthermore, bubble oscillation near a solid plate is also discussed when the radius of the solid sphere is increased to an infinitely large dimension. Thus, this article renders a comprehensive study of naturally pulsating submerged bubbles in the presence of a nearby solid surface of various kinds.Item Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant(2024) Bhattacharya, Sukalyan (TTU); Bhattacharya, SonalThis article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as ( 1 − r 2 ) − 3 / 2 and ( 1 − r 2 ) − 2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.