Recent Research Articles
- Periodic Solutions of the Compressible Euler Equations and the Nonlinear Theory of Sound,
Distinguished Colloquia, City University of Hong Kong, Chinese University of Hong Kong, April 13 & 17, 2023.
- On the Regularity Implied by the Hypotheses of Geometry,
Mathematics Colloquium, University of California Berkeley, October 28, 2021.
Zoom Recording: https://berkeley.zoom.us/rec/share/fwvVqesd7omXCkcd2fBVYGuRt8QQrn0I0NuYgfrlTsMyTItIbDKMAS1RQ6kOCMnF.V_XNVHi46C89sPO0 Passcode: 2$nCr.C@
- How to Smooth a Crinkled Map of Spacetime,
arXiv:1812.06795v5 [gr-qc] 7 Nov 2020 Published RSPA, 16 Sept, 2020.
- On the Regularity Implied by the Assumptions of Geometry,
arXiv:1912.12997 [gr-qc] 26 Nov 2020
- Optimal Metric Regularity in General Relativity follows from the RT-equations by Elliptic Regularity Theory in Lp-spaces,
arXiv:1808.06455v2 [gr-qc] 23 Aug 2018, To appear Meth. Appl. Anal.
- The Regularity Transformation Equations: An Elliptic Mechanism for Smoothing Gravitational Metrics in General Relativity,
arXiv:1805.01004v3 [gr-qc] 24 Sep 2018, To appear Adv. Theor. Math. Phys.
- Shock Wave Interactions and the Riemann-flat condition: The Geometry Behind Metric Smoothing and the Existence of Locally Inertial Frames in General Relativity,
arXiv:1610.02390v4 [gr-qc] 22 Aug 2018, Arch. Rat. Mech. Anal., 235, pages 1873-1904 (2020)
- Inversion of a non-uniform difference operator,
arXiv:1810.05718v1 [gr-qc] 12 Oct 2018
- An Instability in the Standard Model of Cosmology creates the Anomalous Acceleration without Dark Energy,
Proc. Roy. Soc., November 22, 2017
- Causal dissipation for the fluid dynamics of ideal gases, Proc. Roy. Soc, April 2017.
- An Alternative Proposal for the Anomalous Acceleration
Surveys in Differential Geometry, Vol. 20 (2015): One Hundred Years of General Relativity, edited by S.T. Yau, Harvard and L. Bieri, Michigan, Einstein Centennial Jubilee.
- No Regularity Singularities exist at points of general relativistic shock wave interaction between shocks from different characteristic families
RSPA, March 20, 2014
- Causal Dissipation and Shock Profiles in the Fluid Dynamics of Pure Radiation
RSPA, March 20, 2014
- Simulation of general relativistic shock wave interactions by a locally inertial godunov method featuring dynamical time dilation
Proc. Roy. Soc. A, Published online, 4 April 2012.
- General Relativistic Self-Similar Waves that induce an Anomalous Acceleration into the Standard Model of Cosmology
Memoirs of the AMS, November 3, 2011.
- A one parameter family of expanding wave solutions of the Einstein equations that induces an anomalous acceleration into the Standard Model of Cosmology
PNAS, August 25, 2009
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Answers to Questions posed by Reporters:
PNAS August 17, 2009
- The Numerical Simulation of General Relativistic Shock Waves
by a
Locally Inertial Godunov Method
Featuring
Dynamical Time Dilation
Zeke Vogler, Doctoral Dissertation, March 2010
- Global Solutions to the Ultra-Relativistic Euler Equations
Brian Wissman, CMP July 2011
- A Paradigm for time-periodic sound wave propagation in the Compressible Euler Equations
Meth Appl Anal, September, 2009
- Time-periodic Linearized solutions of the Compressible Euler Equations and a problem of small divisors
SIAM Jour Math Anal, 2011
- A Liapunov-Schmidt reduction for time-periodic solutions of the Compressible Euler Equations
Meth Appl Anal, (to appear)
- Linear waves that express the simplest possible periodic structure of the compressible Euler equations
Acta Mathematica Scientia, (Special Issue J. Glimm), 2009
- Shock-Wave Interactions in General Relativity
Springer Lecture Notes 2007
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Conference/Seminar Talks
- The Regularity Transformation Equations: How to smooth a crinkled map of spacetime,
Conference on Nonlinear Partial Differential Equations and Applications, University of Michigan, July 9-12,2019.
(In memory of Joel Smoller)
- Causal Dissipation for the Relativistic Fluid Dynamics of Ideal Gases,
UC-Davis, UC-Riverside, UC-Berkeley, 2017.
- An Instability in the Standard Model of Cosmology Creates the Anomalous Acceleration without Dark Energy,
Plenary Address, Harvard, April 8, 2016; Colloquium ETH Zurich, Switzerland, March 24, 2015; Colloquium UCD Mechanical Eng., February 2015; Colloquium UC-Berkeley, October 2014; Colloquium UC-Davis Mathematics October 2014; Plenary Talk Conference in honor of Eitan Tadmore, May 2014.
- Summary
- Applied Mathematics vs Dark Energy,
Plenary Address, National Colloquia of the Brazilian Mathematical Society, Rio De Janeiro, Brazil, July 2015; Invited one hour talk, Spring Western Sectional Meeting of AMS, Special Session on Conservation Laws, April 18, 2015.
- Nonlineaer Resonance 1980-1995 with Eli Isaacson,
Invited hour talk, National Colloquia of the Brazilian Mathematical Society, Rio De Janeiro, Brazil, July 2015.
- Numerical Simulation of GR Shock Waves by a Locally Inertial Godunov Method with Dynamic Time Dilation, University of Wyoming, June 2010, (Workshop on Conservation Laws); Philadephia, August 2010 (SIAM Special Session on Numerical Relativity); Konstanz University, Germany October 2010 (Applied Math Seminar)
- Periodic Solutions of the Compressible Euler Equations, Gehring Professor, University of Michigan
Fall 2007 (2 seminar talks)
- Periodic Solutions of the Compressible Euler Equations, Gehring Professor, University of Michigan
Fall 2007 (Colloquium)
- Numerical Shock-Wave Cosmology,
New Orleans, January 2007
- Shock-Wave Cosmology - Inside a Black Hole,
Academy Public Lecture, Indian National Academy of Sciences, Bangalore, January 2006
- Locally Inertial Glimm Scheme for General Relativity,
Plenary Talk, Stonybrook, July 2004
- Introduction to Shock-Waves and General Relativity,
Three Lectures, Cambridge University, July 2003
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