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231 results on '"Kichenassamy, Satyanad"'

1. The Relativistic Rotation Transformation and the Observer Manifold

Author

Kichenassamy, Satyanad

Subjects
Mathematics - General Mathematics
Abstract

We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore, not a parameterised motion on a background space or spacetime, but is determined by a particular sequence of tetrads related by specific special Lorentz transformations or boosts. Because such Lorentz boosts do not form a group, these tetrads represent distinct observers that cannot put together their local descriptions into a manifold in the usual sense. The choice of observer manifold depends on the dynamical situation under consideration, and is not solely determined by the kinematics. Three examples are given: Franklin's rotation transformation for uniform plane rotation, the Thomas precession of a vector attached to an electron, and the motion of a charged particle in an electromagnetic field. In each case, at each point of its trajectory, there is a distinguished tetrad and a special Lorentz transformation that maps Minkowski space to the spacetime of the local observer on the curve.

Published
2024
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2. Introduction {\`a} l'oeuvre de S. Kichenassamy en Physique Th{\'e}orique

Author

Kichenassamy, Satyanad

Subjects
Physics - History and Philosophy of Physics, Mathematics - Differential Geometry, Mathematics - History and Overview
Abstract

The work of S. Kichenassamy (1926-2015) in Theoretical and Mathematical Physics covers the spectrum of Relativistic Physics: from the clarification of the postulational basis of the two theories of Relativity, to applications to the measurement of proper time, image formation, collision theory, kinetic theory and radiative transfer, or pulsar electrodynamics, to name a few. After brief biographic remarks,we show, by following an argument first formulated in 1963, and developed in a series of papers, that the physical interpretation of General Relativity requires the replacement of the strong equivalence principle by the C-equivalence principle. By giving a mathematical status to the observer, his insight yields new results regarding measurements actual observers can make, both in Special and in General Relativity. Applications are outlined. His contributions to Indology will be discussed elsewhere., Comment: in French

Published
2022

3. Instability of pole singularities for the Chazy equation

Author

Kichenassamy, Satyanad

Subjects
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematics - Complex Variables
Abstract

We prove that the negative resonances of the Chazy equation (in thesense of Painlev\'e analysis) can be related directly to it sgroup-invariance properties. These resonances indicate in this case the instability of pole singularities. Depending on the value of a parameter in the equation, an unstable isolated pole may turn into the familiar natural boundary, or split into several isolated singularities. In the first case, a convergent series representation involving exponentially small corrections can be given. This reconciles several earlier approaches to the interpretation of negative resonances. On the other hand, we also prove that pole singularities with the maximum number of positive resonances are stable. The proofs rely on general properties of nonlinear Fuchsian equations.

Published
2022
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4. Asymptotic Behavior in Polarized {\bf T}$^2$-symmetric Vacuum Spacetimes

Author

Isenberg, James and Kichenassamy, Satyanad

Subjects
General Relativity and Quantum Cosmology, Mathematical Physics, Mathematics - Analysis of PDEs, 83C30, 83C05
Abstract

We use Fuchsian Reduction to study the behavior near the singularity of a class of solutions of Einstein's vacuum equations. These solutions admit two commuting spacelike Killing fields like the Gowdy spacetimes, but their twist does not vanish. The spacetimes are also polarized in the sense that one of the `gravitational degrees of freedom' is turned off. Examining an analytic family of solutions with the maximum number of arbitrary functions, we find that they are all asymptotically velocity-term dominated as one approaches the singularity.

Published
2017
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5. A study of ancient Khmer ephemerides

Author

Vernotte, François and Kichenassamy, Satyanad

Subjects
Physics - History and Philosophy of Physics, Mathematics - History and Overview, Physics - Data Analysis, Statistics and Probability
Abstract

We study ancient Khmer ephemerides described in 1910 by the French engineer Faraut, in order to determine whether they rely on observations carried out in Cambodia. These ephemerides were found to be of Indian origin and have been adapted for another longitude, most likely in Burma. A method for estimating the date and place where the ephemerides were developed or adapted is described and applied.

Published
2017

6. Analytic description of singularities in Gowdy spacetimes

Author

Kichenassamy, Satyanad and Rendall, Alan D.

Subjects
General Relativity and Quantum Cosmology, Mathematics - Analysis of PDEs, 83C75, 83C15, 83C20, 35Q75, 35A20, 83C05
Abstract

We use Fuchsian Reduction to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary functions. Special cases correspond to polarized, or other known solutions. The method provides precise asymptotics at the singularity, which is Kasner-like. All of these solutions are asymptotically velocity-dominated. The results account for the fact that solutions with velocity parameter uniformly greater than one are not observed numerically. They also provide a justification of formal expansions proposed by Grubi\v{s}i\'c and Moncrief.

Published
2017
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7. Breather Solutions of the Nonlinear Wave Equation

Author

Kichenassamy, Satyanad

Subjects
Mathematics - Analysis of PDEs, General Relativity and Quantum Cosmology, Nonlinear Sciences - Pattern Formation and Solitons
Abstract

We construct series solutions to all orders for breathers of Klein-Gordon equations, in powers of an amplitude parameter epsilon, under a sign condition on the coefficients of the expansion of the nonlinearity. All terms may be computed thanks to the properties of a 1D Schr\"odinger equation with two-soliton potential. We prove that this series is free of poles in the unit disc of the complex epsilon plane if and only if the equation is essentially equivalent to the sine-Gordon equation. This appears to be the only result that explains both what makes the sine-Gordon equation special from a PDE point of view, and at the same time, why approximate, long-lived breathers exist. In a related paper (Classical and Quantum Gravity, 25 (2008) 245004 ) we have extended this approach to address the soliton star problem in General Relativity.

Published
2017
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8. Soliton stars in the breather limit

Author

Kichenassamy, Satyanad

Subjects
General Relativity and Quantum Cosmology, Mathematics - Analysis of PDEs, Nonlinear Sciences - Pattern Formation and Solitons
Abstract

This paper presents an asymptotic reduction of the Einstein-Klein-Gordon system with real scalar field ("soliton star problem"). A periodic solution of the reduced system, similar to the sine-Gordon breather, is obtained by a variational method. This tallies with numerical computations. As a consequence, a time-periodic redshift for sources close to the center of the star is obtained.

Published
2017
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9. Control of blow-up singularities for nonlinear wave equations

Author

Kichenassamy, Satyanad

Subjects
Mathematics - Analysis of PDEs, Nonlinear Sciences - Pattern Formation and Solitons, 93B05, 93C20, 35L71
Abstract

While the global boundary control of nonlinear wave equations that exhibit blow-up is generally impossible, we show on a typical example, motivated by laser breakdown, that it is possible to control solutions with small data so that they blow up on a prescribed compact set bounded away from the boundary of the domain. This is achieved using the representation of singular solutions with prescribed blow-up surface given by Fuchsian reduction. We outline on this example simple methods that may be of wider applicability.

Published
2017
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21. Nash–Moser Inverse Function Theorem

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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22. Applications in Differential Geometry

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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23. Boundary Blowup for Nonlinear Elliptic Equations

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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24. Applications in General Relativity

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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25. Distance Function and Hölder Spaces

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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26. Applications in Astronomy

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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27. Applications to Nonlinear Waves

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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28. Convergent Series Solutions of Fuchsian Initial-Value Problems

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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29. Fuchsian Initial-Value Problems in Sobolev Spaces

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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30. Solution of Fuchsian Elliptic Boundary-Value Problems

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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31. General Reduction Methods

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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32. Formal Series

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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33. Introduction

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Caffarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P. L., editor, Mawhin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, and Kichenassamy, Satyanad

Published
2007
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36. Quelques autres exemples de discours apodictique, II

Author

Kichenassamy, Satyanad and Kichenassamy, Satyanad

Subjects
Joan W Scott, Discourse Analysis, Brahmagupta, Aryabhaṭa, Epistemic cultures, Epistémologie historique, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], kuṭṭaka, algebraic identities, [SHS.HISPHILSO] Humanities and Social Sciences/History, Philosophy and Sociology of Sciences, history of mathematics, varga-prakriti, algebra in several variables, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Abstract

The analysis of problematic mathematical texts, particularly from India, has required the introduction of a new category of rigorous discourse, apodictic discourse. In this second part, we show that its introduction clarifies the approach to epistemic cultures. We also show that the notion of to the fantasy echo is relevant in Epistemology, as suggested by J.W.Scott. We then continue our earlier analysis of Brahmagupta’s Prop. 12.21-32 on the cyclic quadrilateral and identify discursive strategies that enable him to convey definitions, hypotheses and derivations encoded in the very structure of the propositions stating his new results. We also show that the statements of mathematical formulae in words also follow definite discursive patterns.

Published
2022

37. Recent Progress on Boundary Blow-up

Author

Kichenassamy, Satyanad, Brezis, Haim, editor, Ambrosetti, Antonio, editor, Bahri, A., editor, Browder, Felix, editor, Cafarelli, Luis, editor, Evans, Lawrence C., editor, Giaquinta, Mariano, editor, Kinderlehrer, David, editor, Klainerman, Sergiu, editor, Kohn, Robert, editor, Lions, P.L., editor, Mahwin, Jean, editor, Nirenberg, Louis, editor, Peletier, Lambertus, editor, Rabinowitz, Paul, editor, Toland, John, editor, Bandle, Catherine, editor, Berestycki, Henri, editor, Brighi, Bernard, editor, Brillard, Alain, editor, Chipot, Michel, editor, Coron, Jean-Michel, editor, Sbordone, Carlo, editor, Shafrir, Itai, editor, Valente, Vanda, editor, and Caffarelli, Giorgio Vergara, editor

Published
2005
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39. Introduction {à} l'oeuvre de S. Kichenassamy en Physique Th{é}orique

Author

Kichenassamy, Satyanad

Subjects
Mathematics - Differential Geometry, Differential Geometry (math.DG), Mathematics - History and Overview, History and Overview (math.HO), Physics - History and Philosophy of Physics, FOS: Mathematics, History and Philosophy of Physics (physics.hist-ph), FOS: Physical sciences
Abstract

The work of S. Kichenassamy (1926-2015) in Theoretical and Mathematical Physics covers the spectrum of Relativistic Physics: from the clarification of the postulational basis of the two theories of Relativity, to applications to the measurement of proper time, image formation, collision theory, kinetic theory and radiative transfer, or pulsar electrodynamics, to name a few. After brief biographic remarks,we show, by following an argument first formulated in 1963, and developed in a series of papers, that the physical interpretation of General Relativity requires the replacement of the strong equivalence principle by the C-equivalence principle. By giving a mathematical status to the observer, his insight yields new results regarding measurements actual observers can make, both in Special and in General Relativity. Applications are outlined. His contributions to Indology will be discussed elsewhere., Comment: in French

Published
2022
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43. Problems

Author

Boal, Jan List, Bevis, Jean H., Sastry, K. R. S., Selby, M., Kabak, Bertram, Schaumberger, Norman, Murty, V. N., Elsner, Thomas E., Trigg, Charles W., Stacy, Robert S., Usiskin, Zalman, Hoehn, Milton H., Singh, Sahib, Ecker, Michael, Bernet, Charles, Wales, Thomas C., Sastry, K. R. S., Finn, Michael V., Kichenassamy, Satyanad, Close, Robert A., Wiener, Joseph, Bissinger, Barney, and Battles, Frank P.

Published
1982
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