Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

  Degrees & Accolades

Ph.D. Mechanical Engineering (University of Pittsburgh, 2016)
Ph.D. Mathematics (Università del Salento, 2012)

 

  Research Profile

Applied Mathematics, Mathematical Analysis, Partial Differential Equations, Dynamical Systems, Fluid Mechanics and Fluid Dynamics, Mathematical Physics, long-time behavior of solutions to fluid-solid interaction problems, attainability and stability of the equilibrium configurations. Approximation Theory, behavior of interpolating operators on discontinuous functions and approximation of cosine functions by iterates of bounded linear operators.

  Publications

  • On the motion of two rigid bodies with a fluid-filled gap, in preparation. 
  • (with J. Prüss and G. Simonett) On the motion of a fluid-filled rigid body with Navier boundary conditions, submitted (2018). https://arxiv.org/abs/1809.03852
  • (with J. Prüss and G. Simonett) A maximal regularity approach to the study of motion of a rigid body with a fluid-filled cavity, submitted (2018). https://arxiv.org/abs/1804.05403
  • (with G. P. Galdi) Stability and long-time behavior of a pendulum with an interior cavity filled with a viscous liquid. RIMS Kôkyûroku Proceedings No. 2058, Mathematical Analysis of Viscous Incompressible Fluid,  2018, 90--107. 
  • (with G.P. Galdi and M. Mohebbi) On the motion of a liquid-filled heavy body around a fixed point. Quart. Appl. Math., 76 (1), (2018) pp. 113-145. Published electronically on October 4, 2017.
  • (with K. Disser, G.P. Galdi, and P. Zunino) Inertial motions of a rigid body with a cavity filled with a viscous liquid. Arch. Rational Mech. Anal., 221 (1), (2016) 487-526. 
  • (with G.P. Galdi) On the motion of a pendulum with a cavity entirely filled with a viscous liquid. Recent progress in the theory of the Euler and Navier-Stokes Equations, London Mathematical Society Lecture Note Series: 430, Cambridge University Press, 2016, pp. 37-56.
  • (with G.P. Galdi and M. Mohebbi) On the motion of a liquid-filled rigid body subject to a time-periodic torque. Ch. in Recent Developments of Mathematical Fluid Mechanics, Springer Basel, Basel, 2016, pp. 233-255.
  • (with G.P. Galdi and P. Zunino) Inertial Motions of a Rigid Body with a cavity filled with a viscous liquid. https://arxiv.org/abs/1405.6596 (2014).
  • (with G.P. Galdi and P. Zunino) Inertial motions of a rigid body with a cavity filled with a viscous liquid. Comptes Rendus Mécanique 341, (2013) 760–765.
  • (with M. Campiti and C. Tacelli) On the interpolation of discontinuous functions. Journal of Approximation Theory 164, (2012) 731–753.
  • (with M. Campiti and C. Tacelli) Approximation of cosine functions and Rogosinski type operators. Studia Universitatis Babeş-Bolyai. Mathematica 56, (2011) 261–272.
  • (with M. Campiti and C. Tacelli) Behavior of bivariate interpolation operators at points of discontinuity of the first kind. Note di Matematica dell’Università del Salento 31, (2011) 43–66. 

  Conference Talks

  • On the stability and long-time behavior of fluid-solid systems. Applied Math Colloquium, Penn State University, November 26, 2018. 
  • On the inertial motion of a fluid-filled rigid body with Navier boundary conditions. Special Session: Recent Advances in Mathematical Fluid Mechanics, AMS Fall Southeastern Sectional Meeting, University of Arkansas, November 3-4, 2018. 
  • On the inertial motion of a fluid-filled rigid body with partial-slip boundary conditions. Special Session: Recent Developments in Mathematical Analysis of Some Nonlinear Partial Differential Equations, AMS Fall Central Sectional Meeting, University of Michigan, October 20-21, 2018. 
  • On the motion of rigid bodies with a fluid-filled gap. Special Session: Partial Differential Equations and New Perspective of Variational Methods, AMS Spring Southeastern Sectional Meeting, Vanderbilt University, April 14-15, 2018.
  • Long-time behavior and stability of rigid bodies with a fluid-filled gap. MS14: Free Boundary Problems and Fluid Interfaces, SIAM Conference on Analysis of Partial Differential Equations 2017, The Baltimore Convention Center, Baltimore USA, December 9-12, 2017. 
  • Stability and long-time behavior of a heavy rigid body with a cavity completely filled with a viscous liquid. 2017 Midwestern Workshop on Asymptotic Analysis, IUPUI Indianapolis, USA, October 6-8, 2017. 
  • Long-time behavior of rigid bodies with a fluid-filled gap. Special Session: Free-boundary Fluid Models and Related Problems, AMS Spring Southeastern Sectional Meeting, College of Charleston, Charleston USA, March 10-12, 2017. 
  • Asymptotic behavior of rigid bodies with a liquid-filled gap. PDE seminar, Department of Mathematics, Vanderbilt University, Nashville USA, October 7, 2016.
  • On the motions of a liquid-filled rigid body around a fixed point. International Conference on Evolution Equations, Vanderbilt University, Nashville USA, May 16-20, 2016. 
  • On the motions of a liquid-filled pendulum. Conference Numerical Analysis and Predictability of Fluid Motion, Department of Mathematics, University of Pittsburgh, USA, May 3-4, 2016.
  • On the inertial motions of liquid-filled rigid body with slip boundary conditions. Particles in Flows, Summer School & Workshop, Institute of Mathematics of the Academy of Sciences of Czech Republic, Prague Czech Republic, August 25-31, 2014.
  • On the dynamics of a fluid-filled rigid body: inertial and periodic motions. Seminar at the Department of Mathematics and Physics, Università del Salento, Lecce Italy, July 1, 2013.
  • Inertial motions of a rigid body with a liquid-filled cavity. Workshop on Navier-Stokes Equations, Institute for Mathematics RWTH Aachen University, Aachen Germany, May 21-24, 2013. 
  • On the inertial motions of fluid-filled rigid body with slip boundary conditions. The 34th Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE 2014), The University of Memphis, Memphis USA, October 11-12, 2014. 
  • On the inertial motions of liquid-filled rigid bodies. 66th Annual Meeting of the APS Division of Fluid Dynamics, Pittsburgh USA, November 24-26, 2013.
  • On the interpolation of discontinuous functions. Second International Conference on Numerical Analysis and Approximation Theory (NAAT 2010), Babeș-Bolyai University, Department of Applied Mathematics of Faculty of Mathematics and Computer Science, Cluj-Napoca Romania, September 23-26, 2010. 

  Grants

National Science Foundation (Analysis Program) conference grant: "2018 Shanks Workshop on Mathematical Aspects of Fluid Dynamics". Role: Co-Principal Investigator.
Amount: $12,000.
Period: 03/01/2018 – 02/28/2019.