Analysis and Theoretical Physics


Coordinator:
Paulo Vargas Moniz

Group: 
Alberto Manuel Tavares Simões
António Jorge Gomes Bento
César Augusto Teixeira Marques da Silva
Hélder Soares Vilarinho
João Pedro de Jesus Marto
João Pinheiro da Providência e Costa
Mário Júlio Pereira Bessa da Costa 
Mariam Bouhmadi-Lopez
Paulo Jorge dos Santos Pinto Rebelo

Rui Manuel Pires Almeida
Seyed Meraj Mousavi Rasouli 

Collaborators:

Paulo André de Paiva Parada
Rui Jorge Mendes Robalo
José Carlos Duque.
Sandra Cristina de Pinto Vaz Ramos
Vadim Yurinsky (Iourinski)
Sravan Kumar
Yaser Tavakoli 

ATP group develops its activities in Theoretical Physics, Dynamical Systems and PDEs. More specifically, the following topics are investigated:
• Whether (and how) the explicit presence of supersymmetry in gravitational settings will affect the states of the universe, as far as space-time singularities (initial or late time) would be present or not.
• Establish how additional fields (eg, 3-forms) as well as modifications into the Einstein-Hilbert action, namely in the gravitational sector will emerge into observational consequences
• Stability of mechanical systems, geodesic flows, and Poisson Morphisms, in particular stability of dynamical systems exhibiting some symmetry;
• Decay of correlations on random perturbations of asymptotically expanding dynamical systems;
• Stability of nonautonomous dynamic equations with generalized dichotomies on time scales or measure chains, including nonautonomous epidemic models and nonautonomous neural network models on time scales;
• Wave diffraction problems from an operator theory viewpoint and Fredholm property characterization of classes of operators associated to the diffraction problems;
• Approximate solutions to initial boundary value problems using Adomian decomposition method;
• Study nonautonomous epidemic models using optimal control theory



PUBLICATIONS 

2014

A.J.G. Bento, C.M. Silva (2014) Nonuniform dichotomic behavior: Lipschitz invariant manifolds for ODEs Bull. Sci. Math.,138 (1), 89-109. 

Moniz, P.V. Quantum Cosmology: Meeting SUSY, Progress in Mathematical Relativity, Gravitation and Cosmology, Springer Proceedings in Mathematics & Statistics. Volume 60, 2014, pp 117-125.

R. M. Almeida, José C. M. Duque, J. Ferreira¸ R. J. Robalo The Crank-Nicolson-Galerkin finite element method for a class of nonlinear parabolic equations with moving boundaries  Numerical Methods for Partial Differential Equations  (2014) DOI: .

José C. M. Duque, Rui M. P. Almeida, and Stanislav N. Antontsev, Application of the Moving Mesh Method to the Porous Medium Equation With Variable Exponent, Mathematics and Computers in Simulation (2014).DOI.

R. J. Robalo, R. M. Almeida, M. C. Coimbra and J. Ferreira. A reaction- diffusion model for a class of nonlinear parabolic equations with moving boundaries: existence, uniqueness, exponential decay and simulation Applied Mathematical Modelling 38(23):5609-5622. (2014) DOI.

 

José C. M. Duque, Rui M. P. Almeida and Stanislav N. Antontsev. Numerical study of the porous medium equation with absorption, variable exponents of nonlinearity and free boundary. Applied Mathematics and Computation 235 (2014), 137–147. DOI:


2013 


Alves, J.F. and Vilarinho, H. (2013). Strong stochastic stability for non-uniformly expanding maps. Ergodic Theory and Dynamical Systems, 33 (3), 647-612. 

A.J.G. Bento, C.M. Silva (2013) Generalized nonuniform dichotomies and local stable manifolds. Journal of Dynamics and Differential Equations, 25(4), 1139-1158.

António J. G. Bento and César M. Silva, Stable manifolds for nonautonomous equations with nonuniform polynomial dichotomies, Q. J. Math, 63 (2012), 275-308. 

Edgar Pereira, César Silva and Jacques da Silva, A Generalized Non-Autonomous SIRVS Model, Math. Methods Appl. Sci., 36 (2013), 275-289 

J. C. M. Duque, R. M. P. Almeida, and S. N. Antontsev. Convergence of the finite element method for the porous media equation with variable exponent. SIAM Journal on Numerical Analysis, 51(6), 3483-3504.

M. Bessa, J. Rocha and M.J. Torres, Hyperbolicity and Stability for Hamiltonian flows. Journal of Differential Equations, vol 254, 1, 309-322, 2013. 

M. Bessa, J. Rocha and M.J. Torres, Contributions to the geometric and ergodic theory of conservative flows. Ergodic Theory and Dynamical Systems , vol 33, 6, 1709-1731, 2013.

M. Bessa, M. Carvalho, Non-uniform hyperbolicity for infinite dimensional cocycles. Stochastics & Dynamics vol 13, 3, 2013.

M. Bessa, J. Rocha, M. J. Torres, Shades of Hyperbolicity for Hamiltonians. Nonlinearity, vol 26, 10, 2851–2873, 2013.

M. Bessa, On C1-generic chaotic systems in three-manifolds. Qualitative Theory of Dynamical Systems, vol 12, 2, 323–334, 2013

M. Bessa, C1-stably shadowable conservative diffeomorphisms are Anosov. Bulletin of the Korean Mathematical Society. vol 50, 5, 1495–1499, 2013. 

NiK, H., Rebelo, P. and Zahedi, M. (2013). Solution of Infinite Horizon Nonlinear Optimal Control Problems by Piecewise Adomian Decomposition Method. Mathematical Modelling and Analysis, 18 (4), 543-560.

Y. Tavakol, J. Marto, A. H. Ziaie and P.V. Moniz. Semiclassical collapse with tachyon field and barotropic fluid Phys. Rev. D87, 024042 (2013). DOI: 10.1103/PhysRevD.87.024042

Y. Tavakol, J. Marto, A. H. Ziaie and P.V. Moniz. Gravitational collapse with tachyon field and barotropic fluid, General Relat. and Grav. Volume 45, Issue 4, 819-844 (2013). DOI: 10.1007/s10714-013-1503-3



2012 

António J. G. Bento and César M. Silva, Stable manifolds for nonautonomous equations with nonuniform polynomial dichotomies, Q. J. Math, 63 (2012), 275-308.

António J. G. Bento and César M. Silva., Nonuniform $(mu,nu)$-dichotomies and local dynamics of difference equations, Nonlinear Analysis 75 (2012), 78–90. 

Bojowald, M., Kiefer, C. and Moniz, P.V. (2012)
Quantum cosmology for the xxist century: A Debate. 12th Marcel Grossmann Meeting on Recent Dev. in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories - Proc. of the MG 2009 Meeting on General Relativity, pp. 589-608.

Bouhmadi-López, M., Kiefer, C., Sandhofer, B. and Moniz, P.V. (2012)
Defrosting the big freeze quantum mechanically? 12th Marcel Grossmann Meeting on Recent Dev. in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories - Proc. of the MG 2009 Meeting on General Relativity, pp. 1444-1446.

J.C. Fabris, F.T. Falciano, J. Marto and P.V. Moniz.
Dilaton Quantum Cosmology with a Schrödinger-like Equation, Braz. J. of Phys. (2012), 42, Issue 5-6, 475-481. DOI: 10.1007/s13538-012-0105-y

J. M. Azevedo, R. Almeida, P. Almeida, Using data mining with time series data in short-term stocks prediction: a literature review, International Journal of Intelligence Science, 2012.

L. P. Castro, S. Saitoh, Y. Sawano and A.M. Simões. General inhomogeneous discrete linear partial differential equations with constant coefficients on the whole spaces, Complex Analysis and Operator Theory, 6, 307-324, DOI:10.1007/s11785-010-0083-4, 2012.

M. Bessa, J. Rocha, A remark on the topological stability of symplectomorphisms. Applied Mathematics Letters, vol 25, 2, 163-165, 2012.

M. Bessa, C. Silva, Dense area-preserving homeomorphisms have zero Lyapunov exponents. Discrete and Continuous Dynamical Systems – A, vol 32, 4, 1231-1244, 2012.

M. Bessa, Perturbations of Mathieu equations with parametric excitation of large period. Advances in Dynamical Systems and Applications, vol 7, 1, 17-30, 2012.

M. Bessa, M. Carvalho, Frisos imperfeitos de números inteiros (Imperfect friezes of integers). Boletim da Sociedade Portuguesa de Matemática, vol 67, October, 201-208, 2012.

N. Bebiano, J. da Providência, and J. P. da Providência. Tsallis entropies and matrix trace inequalities in quantum statistical mechanics Citation: J. Math. Phys. 53, 103303 (2012); doi: 10.1063/1.4753981

Rebelo, P. (2012). An approximate solution to an initial boundary value problem: Rakib–Sivashinsky equation. International Journal of Computer Mathematics, 89 (7), 881-889. 

Tavakoli,, Y., Moniz, P.V., Marto, J. and Ziaie, A.H. (2012) Loop quantum effect and the fate of tachyon field collapse, J. Phys.: Conf. Ser. 360 012016 doi:10.1088/1742-6596/360/1/012016

2011

J. da Providencia, N. Bebiano, J.P. da Providencia. Non-Hermitian Hamiltonians with Real Spectrum in Quantum Mechanics, Braz. J. Phys (2011) 41:78-85 DOI 10.1007/s13538-011-0010-9

M. Bessa, P. Varandas, On the entropy of conservative flows. Qualitative Theory of Dynamical Systems, vol 10, 1, 11-22, 2011.

M. Bessa, J. Rocha, Denseness of ergodicity for a class of volume-preserving flows. Portugaliae Mathematica, vol 68, 1, 1-17, 2011.

M. Bessa, J. Rocha, Topological stability for conservative systems, Journal of Differential Equations, vol 250, 10, 3960-3966, 2011.

Rebelo, P. (2011). An approximate solution to an initial boundary value problem to the one-dimensional Kuramoto-Sivashinsky equation, International Journal for Numerical Methods in Biomedical Engineering 27 (6) , pp. 874-881.

S. M. M. Rasouli, M. Farhoudi and H. R. Sepangi. An isotropic Cosmological model in Modifed Brans-Dicke Theory , Class. Quantum Grav. 28 (2011) 155004.

S. M. M. Rasouli, N. Khosravi and M. Farhoudi . Horizon problem remediation via deformed phase space, Gen Relativ Gravit (2011) 43:2895–2910


2010

J. P. da Providência. Three Branch Normal Mode Dispersion Relation for Metals: The case of large momentum transfer, Solid State Communications 150 (2010) 54-57

M. Bessa, J. Rocha, Three-dimensional conservative star flows are Anosov, Discrete and Continuous Dynamical Systems – A , vol 26, 3, 839-846, 2010.

M. Bessa, C. Ferreira, J. Rocha, On the stability of the set of hyperbolic closed orbits of a Hamiltonian, Mathematical Proceedings of the Cambridge Philosophical Society, vol 149, 2, 373-383, 2010.

Mariam Bouhmadi-Lopez, Yaser Tavakoli, Paulo Vargas Moniz. Appeasing the Phantom Menace?, JCAP 1004 (2010) 016 DOI: 10.1088/1475-7516/2010/04/016

N. Bebiano, J. da Providência and J.P. da Providência. Classes of non-hermitian operators with real eigenvalues. Electron. J. Linear Algebra 21 (2010), 98-109. 

Moniz, P.V. Quantum cosmology - the supersymmetric perspective : Vol. 1: Fundamentals, Lect.Notes Phys. 803 (2010) 1-351 DOI: 10.1007/978-3-642-11575-2 

Moniz. P.V. Quantum Cosmology - The Supersymmetric Perspective : Vol. 2 Advanced Topic Published in Lect.Notes Phys. 804 (2010) 1-283 DOI: 10.1007/978-3-642-11570-7

Moniz, P.V. and Ward, J. (2010) Gauge field back-reaction in Born–Infeld cosmologies, Class. Quantum Grav. 27 235009 doi:10.1088/0264-9381/27/23/235009

Rebelo, P. On the approximate solution to an initial boundary valued problem for the Cahn–Hilliard equation, Communications in Nonlinear Science and Numerical Simulation, Volume 15, Issue 2, February, 2010, P. 225-231

S. M. M. Rasouli, S. Jalalzadeh. On the energy conditions in non-compact Kaluza-Klein gravity. Annalen der Physik, (Berlin) 19, 276 (2010).


2009

Barreira, L., Silva, C. and Valls, C. (2009) Nonuniform Behaviour and Robustness, J. Differential Equations, 246, 3579-3608.

Bento, A. and Silva, C. (2009) Stable Manifolds for Nonuniform Polynomial Dichotomies, J. Funct. Anal., 257, 122-148.

Claus Kiefer, Joao Marto, Paulo Vargas Moniz (2009). Indefinite oscillators and black-hole evaporation Annalen Phys. 18, 722-735 DOI: 10.1002/andp.200910366.

Dias, João L; Bessa, Mário. 2009. "Hamiltonian elliptic dynamics on symplectic 4-manifolds", Proceedings of the American Mathematical Society, 137: 585 - 592.

M. Bessa, J. L. Dias, Hamiltonian elliptic dynamics on symplectic 4-manifolds, Proceedings of the American Mathematical Society, vol. 137, 585-592, 2009.

M.Bessa, Are there chaotic maps in the sphere? Chaos, Solitons & Fractals, vol. 42, nº1, 235-237, 2009.

M. Bessa, J. Rocha, Homoclinic tangencies versus uniform hyperbolicity for conservative 3-flows, Journal of Differential Equations, vol. 247, 2913-2923, 2009.

Mariam Bouhmadi-Lopez, Claus Kiefer, Barbara Sandhofer, Paulo Vargas Moniz. On the quantum fate of singularities in a dark-energy dominated universe ,Phys.Rev. D79 (2009) 124035 DOI: 10.1103/PhysRevD.79.124035

N. Doroud, S. M. M. Rasouli and S. Jalalzadeh. A class of cosmological solutions in induced matter theory with conformally fat bulk space. GRG 41 2637 (2009).

Paulo Vargas Moniz, Sudhakar Panda, John Ward. Higher order corrections to Heterotic M-theory inflation, Class.Quant.Grav. 26 (2009) 245003 DOI: 10.1088/0264-9381/26/24/245003

S. M. M. Rasouli, A. F. Bahrehbakhsh, S. Jalalzadeh, and M. Farhoudi. Quantum mechanics and geodesic deviation in the brane world. EPL, 87, 40006 (2009).


2008

J. Marto. The Franson experiment revisited, Phys. Lett. A 372,(2008), 6872-6874. DOI: 10.1016/j.physleta.2008.10.010

J. P. da Providência. Collective modes in metals: quantal and semiclassical approaches,
J. Phys.: Condens. Matter, 20 (2008) 485219 (6pp).

Mariam Bouhmadi-Lopez, Paulo Vargas Moniz. Phantom-like behaviour in a brane-world model with curvature effects Phys.Rev. D78 (2008) 084019 DOI: 10.1103/PhysRevD.78.084019

M. Bessa, Dynamic of generic multidimensional linear differential systems, Advanced Nonlinear Studies, Vol 8, 191-211 , 2008.

M. Bessa, J. Rocha, On the fundamental regions of a fixed point free conservative Hénon map, Bulletin of the Australian Mathematical Society, Vol 77, nº 1, 37-48, 2008.

M. Bessa, J. L. Dias, Generic dynamics of 4-dimensional C2 Hamiltonian systems, Communications in Mathematical Physics, Vol 281, nº 1, 597-619, 2008.

M. Bessa, P. Duarte, Abundance of elliptic dynamics on conservative 3-flows, Dynamical Systems – An international Journal, Vol 23, nº 4, 409-424, 2008.

M. Bessa, J. Rocha, On C1-robust transitivity of volume-preserving flows , Journal of Differential Equations, vol. 245 – 11, 3127-3143, 2008.

M. Bessa, M. Carvalho, On the spectrum of infinite dimensional random products of compact operators , Stochastics & Dynamics, vol. 8 – 4, 593-611, 2008.

M. Bessa, Generic incompressible flows are topological mixing, Comptes Rendus Mathematique vol. 346, 1169-1174, 2008.

V. Araújo, M. Bessa, Dominated splitting and zero volume for incompressible three-flows, Nonlinearity, Vol 21, nº 7, 1637-1653, 2008.

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