Lalit A Patel

Lalit A Patel's Resaerch Papers

Papers marked @ were poorly (or not) peer-reviewed. Papers marked # are poorly (or not) indexed.

1 @ #
Extension of the Principle of Mathematical Induction
LAPatel
The Journal of the Maharaja Sayajirao University of Baroda
v 21 y 1972 n 3 p 87-89
Lipy GoogleSch
Principle of mathematical induction has been explored over the sets of all integers, all rational numbers, all real numbers and all complex numbers. This has been done as a natural extension of the known induction principle for the set of all positive integers.


2
Ion-Acoustic Solitons in an Electromagnetically Irradiated Magnetoplasma
LAPatel
Journal of Plasma Physics
v 18 y 1977 n 3 p 381-389
Lipy DOI Journal GoogleSch ResGate
We have investigated how the presence of an electromagnetic beam and a static magnetic field influences the ion-acoustic solitons in a plasma. A modified KdV equation is derived in which the electromagnetic field plays the role of a source term. By using the perturbation analysis technique, it is shown that a homogeneous electromagnetic beam does not destabilize the ion-acoustic solitons; it reduces the amplitude, but not the velocity, of the solitons. However, any inhomogeneity in the electromagnetic field intensity does destabilize the ion-acoustic solitons; albeit not to an appreciable extent for typical cases.


3
Effect of Self-Focusing on Scattering of a Laser Beam in a Collisional Plasma
LAPatel
Journal of Physics D Applied Physics
v 11 y 1978 n 3 p 347-354
Lipy DOI Journal GoogleSch ResGate
The temporal growth rates of stimulated Raman and Brillouin scattering of a self-focused laser beam in a collisional plasma have been evaluated. The calculations predict a considerable spatial nonuniformity in the scattering because of the temperature and density gradients induced in the plasma on account of the nonuniformity of the pump laser beam.


4
Self-Induced Transparency of a Two-Frequency Pulse
LAPatel
Optik
v 50 y 1978 n p 243-247
Lipy GoogleSch
The two modes of two frequency electromagnetic pulse are parametrically coupled in a medium which is resonantly absorbing at these two frequencies. It is found that the pulse can pass undistorted provided the initial electric field-amplitude () be large enough, and the effective refrective index () be the same for both the modes.


5
Temporal Growth of a Parametric Excitation by a Self-Focused Laser Beam
LAPatel
Optical and Quantum Electronics
v 10 y 1978 n 3 p 189-194
Lipy DOI Journal GoogleSch ResGate
The effect of self-focusing of the pump laser beam on the temporal growth of a parametric excitation has been investigated in the paraxial region. The two equations for the signal and idler modes have been decoupled by assuming the near self-trapping condition and a linearly varying phase mismatch. By employing the WKBJ approximation, it is found that the growth rate is a strong function of the radial intensity inhomogeneity of the pump laser beam. The condition for validity of the first-order approximate theory employed here has been derived.


6
Effect of Nonlinear Absorption on Self-Focusing of a Laser Beam in a Plasma
MSSodha, LAPatel, RPSharma
Journal of Applied Physics
v 49 y 1978 n p 3707-3713
Lipy DOI Journal GoogleSch ResGate
Considering both the real and imaginary parts of the dielectric constant to be intensity dependent, we have investigated the self‐focusing of a Gaussian laser beam in a plasma. The mechanism or nonlinearity considered herein is the ponderomotive force or heating mainly determined by collisions of electrons with heavier particles. An equation for the beamwidth parameter and an expression of the axial intensity have been obtained in the WKB(J) and paraxial approximations. It is seen that the effect of nonlinear absorption on self‐focusing is significant. Consideration of nonlinearity in absorption predicts focusing of a laser beam (under certain conditions) even when the linear‐absorption approximation would predict defocusing of the beam. The results reduce to the corresponding analytical results reported earlier, when the intensity dependence of the dielectric constant is neglected. The technique adopted in the present investigation for solving the wave equation in the presence of nonlinear absorption is equally applicable to media other than a plasma.


7
Self-Focusing of a Laser Pulse in a Transient Plasma
MSSodha, LAPatel, DPTewari
Journal of Plasma Physics
v 19 y 1979 n 2 p 301-312
Lipy DOI Journal GoogleSch ResGate
Following Akhmanov's approach, self-focusing of a laser pulse in a transient plasma has been studied. The beamwidth parameter and hence the laser intensity and the frequency shift (time derivative of the phase) have been evaluated as a function of time and the distance of propagation. It is seen that the time dependence of the axial intensity changes appreciably as the pulse propagates. The present investigation is restricted to a pulse whose incident intensity has Gaussian radial dependence.


8
Self-Focusing of a Laser Beam in an Inhomogeneous Plasma
MSSodha, LAPatel, SCKaushik
Plasma Physics
v 21 y 1979 n 1 p 1--12
Lipy DOI Journal GoogleSch ResGate
Considering both the real and imaginary parts of the dielectric constant to be intensity dependent, we have investigated the self‐focusing of a Gaussian laser beam in a plasma. The mechanism or nonlinearity considered herein is the ponderomotive force or heating mainly determined by collisions of electrons with heavier particles. An equation for the beamwidth parameter and an expression of the axial intensity have been obtained in the WKB(J) and paraxial approximations. It is seen that the effect of nonlinear absorption on self‐focusing is significant. Consideration of nonlinearity in absorption predicts focusing of a laser beam (under certain conditions) even when the linear‐absorption approximation would predict defocusing of the beam. The results reduce to the corresponding analytical results reported earlier, when the intensity dependence of the dielectric constant is neglected. The technique adopted in the present investigation for solving the wave equation in the presence of nonlinear absorption is equally applicable to media other than a plasma.


9
Average Field of a Laser Beam Self-Focused in a Turbulent Plasma
MSSodha, LAPatel
Journal of Applied Physic
v 51 y 1980 n 5 p 2381-2386
Lipy DOI Journal GoogleSch ResGate
This paper presents an investigation on the spatial variation of the average field of a laser beam which is self‐focused in a plasma having random fluctuations in its electron concentration. The analysis is valid for the arbitrary mechanism of self‐focusing nonlinearity, for nonlinearly absorbing and nonuniform plasmas, and for elliptically Gaussian laser beams. The Novikov‐Furutsu formalism has been followed to derive a parabolic equation for the average field, and the Akhmanov approach has been employed to solve this equation. It is concluded that the plasma turbulence tends to reduce the field intensity as the laser beam penetrates further. The self‐focusing‐induced oscillations of the beamwidth parameters and axial intensity become considerably aperiodic in the presence of turbulence; after a sufficient distance of propagation, an oscillating beamwidth parameter (axial intensity) starts increasing (decreasing) monotonically.


10
Self-Focusing of a Laser Beam in a Magnetoplasma
LAPatel, MSSodha
Journal of Modern Optics (fka Optica Acta)
v 27 y 1980 n 6 p 783-787
Lipy DOI Journal GoogleSch ResGate
This paper presents an investigation of the self-focusing of an elliptically gaussian laser beam propagating along the static magnetic field in a non-linearly absorbing magnetoplasma. The electron concentration and temperature and the static magnetic field are allowed to be non-uniform. The direct coupling as well as the indirect coupling between the right- and left-handedly polarized modes has been taken into account. Coupled equations for the beamwidth parameters have been derived by using the Akhmanov approach. It is seen that axial symmetry of the intensity distributions of the two modes is not preserved in the presence of the direct coupling. The variations of the beamwidth parameters become considerably aperiodic on account of the indirect coupling and non-uniformity in the plasma parameters. Though the investigation is explicitly related to a magnetoplasma, the analysis presented herein can be easily extended for some other anisotropic media.


11
Parametric Interaction of Radially-Gaussian Modes in the Absence of Self Focusing
LAPatel, MSSodha
Journal of Physics D Applied Physics
v 14 y 1981 n 8 p 1385-1394
Lipy DOI Journal GoogleSch ResGate
The authors present an investigation on the effect of transverse non-uniformity on the parametric interaction of radially gaussian modes of arbitrary type in the absence of self-focusing. The propagation-distance dependences of the real-valued axial amplitudes, phases, beamwidth parameters and phase gradients have been derived by using the variational technique. The analysis has been numerically illustrated by considering the stimulated Raman scattering in a plasma. It is seen that the pump node propagates like a trapped filament whereas the remaining modes undergo a periodic focusing or defocusing on account of the parametric-interaction-induced energy exchange.


12
Second-Harmonic Generation in a Graded-Density Plasma Containing a Colloidal Net
LAPatel
Journal of Applied Physics
v 52 y 1981 n p 4982-4984
Lipy DOI Journal GoogleSch ResGate
An experimental scheme is proposed to enhance the second‐harmonic generation. It consists of a cylindrical waveguide filled with a graded‐density plasma and containing a colloidal net whose atoms form a two‐level system. An intense laser pulse incident on the waveguide propagates inside and ’’halts’’ in the colloidal net where it excites the atoms by the two‐photon absorption mechanism. The subsequent stimulated emission yields a radiation at double the initial frequency.


13 @ #
Non-Wkb Variational Theory of Self-Focusing of an Elliptically Gaussian Laser Beam in a Plasma
MSSodha, LAPatel
Proceedings-Indian National Science Academy. Part A, Physical Sciences
v 48 y 1982 n 2 p 194-197
Lipy Journal GoogleSch ResGate
This paper presents a non-WKB variational treatment of the self-focusing of an illiptically Gaussian laser beam in an axially-inhomogeneous plasma. Six coupled second-order ordinary differential equations have been obtained for the axial amplitude, beam width parameters and coefficients. These equations have been compared with the WKB Akhmanov-approach equations. It is shown that the concept of a wave number is not strictly valid in the overdense region where the electric field of the laser beam varies highly nonsinusoidally.


14 @ #
Economics of Wood Energy in India
LAPatel, BMishra, LLPatel
Urja (Indian Journal of Energy)
v 1982 y 1982 n 6 p 1--2
Lipy
This paper presents a model for the development of wood energy in India. According to the model, energy-rich trees are grown on the land spared by villages and also on land presently lying idle on both sides of the raiway/road route. This scheme makes the best possible use of land. avoids future mishaps, and makes wood available to all sections and citizens. The paper then presents an economic analysis of the proposed model. Necessary algebraic expressions are derived, and a graphic presentation thereof is given, whereby it is possible to estimate the product thresholds and profitability ranges under different conditions.


15 @ #
Animal-Driven Modular Biogas Plant
LAPatel
Urja (Indian Journal of Energy)
v 1985 y 1985 n 12 p 321-322
Lipy
This paper presents a generized description of a new design for the biogas plant. In this biogas plant (unlike the conventional ones), the animal urine is better utilized, the animal energy is taken advantage of in the feeding and stirring processes, and the expnasion and interlinking are convenient.


16 @ #
Degumming of Prospis Wood and Briquetting it with Rice Husk
LAPatel
Urja (Indian Journal of Energy)
v 1986 y 1986 n 8 p 82
Lipy
This paper presents a method of making prosopis wood rice husk white coal. Such a white coal offers advantages like gum utilization, good holding strength, tolerable ash content desirable combusion characteristics etc.


17
Virtual Numbers to Represent Entangled Quantum States
LAPatel
Journal of Quantum Information Science
v 4 y 2014 n p 42934
Lipy DOI Journal GoogleSch ResGate
In the existing formalism of quantum states, probability amplitudes of quantum states are complex numbers. A composition of entangled quantum states, such as a Bell state, cannot be decomposed into its constituent quantum states, implying that quantum states lose their identities when they get entangled. This is contrary to the observation that a composition of entangled quantum states decays back to its constituent quantum states. To eliminate this discrepancy, this paper introduces a new type of numbers, called virtual numbers, which produce zero upon multiplication with complex numbers. In the proposed formalism of quantum states, probability amplitudes of quantum states are general numbers made of complex and virtual numbers. A composition of entangled quantum states, such as a Bell state, can then be decomposed into its constituent quantum states, implying that quantum states retain their identities when they get entangled.


18 @ #
Quantum Entanglement Operator and Space-Time Variation
LAPatel
Academia.edu
y 2014
Lipy Academia
An entanglement operator matrix is introduced for the joint state of two quantum states. Entanglementbetween two particles attenuates as their distance or outward speed increases.


19 #
De Broglie Wave Particle Duality Theory Generalized to Reinterpret the Quantum Linear Superposition Principle
LAPatel
International Conference to Commemorate 100 Years of Matter Waves
y 2023 Accepted as Poster
Lipy
This paper generalizes de Broglie’s wave-particle duality theory. According to this generalized model, each physical quantity of a quantum object has certain allowed states, and the quantum object keeps on making periodic oscillations among these allowed states. The quantum linear superposition principle should be interpreted to imply that the quantum object passes through all of its allowed states during the course of its journey in time. The amplitude coefficients of the linear superposition should be interpreted as fractions of times spent by the quantum object in various allowed states. Measured values show randomness because measurements yield results based on their timings and since measurements are timed randomly at the quantum scale. Thus, this paper removes the measurement bias and the over-probabilistic viewpoint of quantum mechanics. The paper then casts and interprets the quantum entanglement phenomenon in terms of synchronous oscillations. Two objects are seen to be quantum entangled because they have similar allowed states and their cycles of oscillations among their allowed states are matching precisely mainly due to their initial conditions. This interpretation does not depict quantum entanglement as a spooky action at a distance, and thereby resolves the EPR paradox. This interpretation can be verified using an experiment similar to quantum entanglement experiments conducted so far. This interpretation has many far-reaching implications. It can have numerous applications in the field of quantum computing. New and better quantum computers can be designed using quantum entanglement due to periodic oscillations.


20 #
Linear Superposition as Temporal Oscillations
LAPatel
Preprint Posted on Optica Open
y 2023 Preprint
Lipy Preprint
The linear superposition principle and the quantum entanglement phenomenon play crucial roles in the fields of quantum computing and information. Their current interpretations are not satisfactory. To reduce the measurement-bias of the current interpretation, this paper presents an alternative interpretation for the quantum linear superposition principle: A physical quantity of a quantum object keeps oscillating between the allowed values of the physical quantity. Thus, a quantum system is inherently deterministic, but it appears to be probabilistic because of randomness in timings of measurements. Then, to show that the so-called quantum entangled need not interact or communicate with each other, the paper presents an alternative interpretation of the quantum entanglement phenomenon: Quantum objects appear to be entangled if and when each physical quantity of these objects undergoes synchronous oscillations. An experimental method is presented to validate this interpretation. Quantum entanglement due to synchronous oscillations can lead to more and better ways of emulated quantum computers. A possible schema of an emulated quantum computer is presented.


21 @
Quantum Computing with Oscillatory Quanta
LAPatel
Proceedings of SPIE 129110F Quantum Computing Communication and Simulation IV (ed by PRHemmer and AL Migdall)
y 2024 p 1-13
Lipy DOI Journal GoogleSch LipyVideo YouTube
The linear superposition principle and the quantum entanglement phenomenon play crucial roles in the fields of quantum computing and information. Their current interpretations are not satisfactory for the need of quantum computing and information. To reduce the measurement-bias of the current interpretation of the quantum linear superposition principle, this paper presents an alternative interpretation: A physical quantity of a quantum object keeps oscillating between the allowed values of the physical quantity. Thus, a quantum system is inherently deterministic, but it appears to be probabilistic because of randomness in timings of measurements. Then, to show that the so-called quantum entangled objects need not interact or communicate with each other, the paper presents an alternative interpretation of the quantum entanglement phenomenon: Quantum objects appear to be entangled if and when each physical quantity of these objects undergoes synchronous oscillations. An experimental method is presented to validate this interpretation. Quantum entanglement due to synchronous oscillations can lead to more and better ways of quantum computers. The paper introduces Excel and Python quos package approaches to simplify and expedite designing and simulating quantum computing circuits.