Publications
32. F. Scabbia, C. Gasparrini, M. Zaccariotto, U. Galvanetto, A. Larios, F.Bobaru Moving interfaces in peridynamic diffusion models and influence of discontinuous initial conditions: Numerical stability and convergence (submitted)
31. M. Enlow, A. Larios, J. Wu, Algebraic calming for the 2D Kuramoto-Sivashinsky equations (submitted) [arXiv]
30. E. Carlson, A. Larios, E. S. Titi, Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: The 2D Navier-Stokes equations paradigm. (submitted) [arXiv]
29. A. Larios, Y. Pei, C. Victor, The second-best way to do sparse-in-time continuous data assimilation: Improving convergence rates for the 2D and 3D Navier-Stokes equations. (submitted) [arXiv]
28. A. Farhat, A. Larios, V. R. Martinez, J. P. Whitehead, Identifying the body force from partial observations of a 2D incompressible velocity field. (submitted) [arXiv]
27. J. Zhao, A. Larios, F. Bobaru, Construction of a peridynamic model for viscous flow. J. Comp. Physics 468 (2022) Paper No. 111509, 16 pp. [SSRN]
26. T. Franz, A. Larios, C. Victor, The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations. Comput. Methods Appl. Mech. Engrg., 392 (2022) Paper No. 114673, 19 pp. [arXiv]
25. E. Carlson, J. Hudson, A. Larios, V. R. Martinez, E. Ng, J. P. Whitehead, Dynamically learning the parameters of a chaotic system using partial observations. Discrete Contin. Dyn. Syst. 42 (2022), no.~8, 3809-3839 [arXiv]
24. S. Jafarzadeh, F Mousavi, A. Larios, F. Bobaru, A general and fast convolution-based method for peridynamics: Applications to elasticity and brittle fracture. Comput. Methods Appl. Mech. Engrg., 392 (2022) Paper No. 114666, 36 pp. [arXiv]
23. E. Carlson, L. Van Roekel, H. Godinez, M. Petersen, A. Larios, Exploring a New Computationally Efficient Data Assimilation Algorithm For Ocean Models. (submitted)
22. A. Larios, M. M. Rahman, K. Yamazaki, Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three. J. Nonlinear Sci. 32(6) (2022), 1–33. [arXiv]
21. E. Carlson, A. Larios. Sensitivity analysis for the 2D Navier-Stokes equations with applications to continuous data assimilation. J. Nonlin. Sci., 31, 5, (2021). [arXiv]
20. S. Jafarzadeh, L. Wang. A. Larios, F. Bobaru, A fast convolution-based method for peridynamic transient diffusion in arbitrary domains. Comput. Methods Appl. Mech. Engrg., 375, Paper No. 113633, (2021). [arXiv]
19. M. Gardner, A. Larios, L.G. Rebholz, D. Vargun, C. Zerfas, Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations. AIMS Electronic Research Archive. 29, no. 1 (2021), 2223-2247.
18. A. Larios, C. Victor, Continuous data assimilation with a moving cluster of data points for a reaction diffusion equation: A computational study. Commun. Comp. Phys. 29 (2021), 1273-1298. [arXiv]
17. A. Larios, K. Yamazaki, On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation. Physica D. 411 (2020), 1-14. [arXiv]
16. S. Jafarzadeh, A. Larios, F. Bobaru, Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methods J. Peridynam. Nonlocal Modeling. 2, no. 1 (2020), 85-110. [arXiv]
15. E. Carlson, J. Hudson, A. Larios, Parameter recovery and sensitivity analysis for the 2D Navier-Stokes equations via continuous data assimilation. SIAM J. Sci. Comput. 42, no. 1 (2020), 250-270. [arXiv]
14. A. Larios, Y. Pei, Nonlinear continuous data assimilation. (submitted) [arXiv]
13. A. Larios, Y. Pei, Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data. Evol. Equ. Control Theory. 9 (2020), no. 3, 733–751. [arXiv]
12. A. Larios, L. G. Rebholz, C. Zerfas, Global in time stability and accuracy of IMEX-FEM data assimilation schemes for the Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 345 (2019), 1077–1093. [arXiv]
11. A. Larios, Y. Pei, L. G. Rebholz, Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations. J. Differential Equations 266 (2019), no. 5, 2435–2465. [arXiv]
10. A. Biswas, J. Hudson, A. Larios, and Y. Pei, Continuous data assimilation for the magnetohydrodynamic equations in 2D using one component of the velocity and magnetic fields. Asymptotic Anal. 108 (2018), no. 1-2, 1-43. [pdf]
9. A. Larios, B. Wingate, M. Petersen, E. S. Titi, The Euler-Voigt equations and a computational investigation of the finite-time blow-up of solutions to the 3D Euler Equations Theor. Comp. Fluid Dyn. 3, no.~1 (2018), 23-34. [arXiv]
8. A. Larios, Y. Pei, On the local well-posedness and a Prodi-Serrin type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion. J. Differential Equations. 263 (2017), no. 2, 1419-1450. [arXiv]
7. A. Biswas, C. Foias, and A. Larios, On the attractor for the semi-dissipative Boussinesq equations. Ann. Inst. H. Poincaré Anal. Non Linéaire. 34 (2017), no. 2, 381-405. [arXiv]
6. A. Larios, E.S. Titi, Some paradigms on the effect Of boundary conditions on the global regularity and singularity of non-linear partial differential equations. Recent progress in the theory of the Euler and Navier-Stokes equations, 96–125, London Math. Soc. Lecture Note Ser., 430, Cambridge Univ. Press, Cambridge, 2016.[arXiv]
5. J.-L. Guermond, A. Larios, T. Thompson, Validation of an entropy-viscosity model for large eddy simulation. Direct and Large-Eddy Simulation IX, ERCOFTAC Series, 20 (2015), 43-48. [pdf] [link]
4. A. Larios and E.S. Titi, Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations. J. Math. Fluid Mech. 16 (2014), no. 1, 59-76. [pdf]
3. A. Larios, E. Lunasin, and E.S. Titi, Global well-posedness for the 2D Boussinesq system without heat diffusion and with either anisotropic viscosity or inviscid Voigt-α regularization. J. Differential Equations. 255 (2013) 2636-2654. [pdf]
2. P. Kuberry, A. Larios, L.G. Rebholz, N.E. Wilson, Numerical approximation of the Voigt regularization of incompressible Navier-Stokes and magnetohydrodynamic flows, Computers & Mathematics with Applications 64(8) (2012), 2647-2662. [pdf]
1. A. Larios and E.S. Titi, On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models, Discrete and Continuous Dynamical Systems B, 14(2) (2010), 603-627. (An invited article for a special issue in honor of Professor P. Kloeden on the occasion of his 60th birthday) [pdf]