Goncalo Apra Sardinha da Cunha Dias

@isel.pt

Área Departamental de Matemática
Instituto Superior de Engenharia de Lisboa/Instituto Politécnico de Lisboa

Goncalo Apra Sardinha da Cunha Dias


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https://researchid.co/gacdias

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematical Physics
20

Scopus Publications

296

Scholar Citations

8

Scholar h-index

6

Scholar i10-index

Scopus Publications

  • Flow of a Periodic Interfacial Travelling Water Wave
    Filipe S. Cal, Gonçalo A. S. Dias
    Water Waves, 2025
    We consider a symmetric periodic travelling wave propagating at the interface between two homogeneous, incompressible, irrotational and inviscid fluids bounded by horizontal planes. For interfacial waves of small amplitude, we present a formula for the interface wave depending on the pressure at the rigid lid and at the flat bottom, and, for the general non-linear case, we derive a lower bound for the interfacial wave height. Under certain conditions imposed on the horizontal component of the motion at the interface and supposing that the horizontal components of the velocity in each layer never reach the wave speed, we study the monotonicity of the horizontal component of the velocity field along the streamlines and also analyze the monotonicity of the pressure along horizontal lines throughout the fluid in both layers, and along the boundary of the domain, between the crest and the trough. Finally, based on the behavior of the velocity field components, we build a pictorial description of the particle paths in both layers.
  • Trapped Modes Along Periodic Structures Submerged in a Three-Layer Fluid with a Background Steady Flow
    Gonçalo A. S. Dias, Bruno M. M. Pereira
    Computation, 2025
    In this study, we study the trapping of linear water waves by infinite arrays of three-dimensional fixed periodic structures in a three-layer fluid. Each layer has an independent uniform velocity field with respect to the fixed ground in addition to the internal modes along the interfaces between layers. Dynamical stability between velocity shear and gravitational pull constrains the layer velocities to a neighbourhood of the diagonal U1=U2=U3 in velocity space. A non-linear spectral problem results from the variational formulation. This problem can be linearized, resulting in a geometric condition (from energy minimization) that ensures the existence of trapped modes within the limits set by stability. These modes are solutions living the discrete spectrum that do not radiate energy to infinity. Symmetries reduce the global problem to solutions in the first octant of the three-dimensional velocity space. Examples are shown of configurations of obstacles which satisfy the stability and geometric conditions, depending on the values of the layer velocities. The robustness of the result of the vertical column from previous studies is confirmed in the new configurations. This allows for comparison principles (Cavalieri’s principle, etc.) to be used in determining whether trapped modes are generated.
  • Velocity and energy of periodic travelling interfacial waves between two bounded fluids
    F.S. Cal, G.A.S. Dias
    Wave Motion, 2023
  • Wave trapping by freely floating obstacles in a discretely stratified fluid
    Filipe S. Cal, Gonçalo A. S. Dias, Bruno M. M. Pereira, Juha H. Videman
    Mathematical Methods in the Applied Sciences, 2023
    In the context of the linear water wave theory, we model the interaction of time‐harmonic water waves with an infinite array of three‐dimensional freely floating bodies in a multilayer fluid through a spectral boundary value problem, consisting of a differential equation coupled with an algebraic system. We present a variational and operator formulation for the problem and derive sufficient conditions for the existence of trapped waves. We give examples of floating obstacles supporting trapped waves in a discretely stratified fluid in different obstacle configurations with a variable number of layers. Some conclusions regarding the dependence of the sufficient condition on the number of fluid layers are drawn, considering whether the sufficient condition is of the potential or algebraic type.
  • Trapped modes along periodic structures submerged in a two-layer fluid with background steady flow
    Gonçalo A. S. Dias
    Mathematical Methods in the Applied Sciences, 2023
    The trapping of linear water waves by infinite arrays of three‐dimensional fixed periodic structures in a two‐layer fluid, where the layers are considered semi‐infinite in depth, have a common interface and move each with an independent uniform velocity with respect to the ground, is studied. The existence of real solutions to the dispersion relation demands a further stability condition on the layer velocities. From the variational formulation, after certain choices of background steady flow, results a nonlinear spectral problem, which upon a sensible linearization gives a geometric condition ensuring the existence of trapped modes (within the limits set by the stability condition). Symmetries reduce the global problem to the first quadrant of the velocity space. Examples are shown of configurations of obstacles that are both independent of the layer velocities and dependent only on their difference. Future developments are suggested.
  • Trapped modes in a fluid with three layers topped by a rigid lid
    Filipe S. Cal, Gonçalo A.S. Dias, Bruno M.A.M. Pereira
    Mathematical Methods in the Applied Sciences, 2022
    We consider trapping of linear water waves by a submerged horizontal cylinder in a three‐layer fluid topped by a rigid lid. Trapped modes correspond to time harmonic oscillations with finite energy of the fluid surrounding a submerged structure and can be found as eigenfunctions of a certain spectral boundary‐value problem. Our main result is a geometric condition relating the cross sections of the submerged parts of the obstacles and the line integrals along the parts of the interfaces pierced by the obstacles and guaranteeing the existence of trapped modes: This follows from variational techniques applied to a suitable operator formulation of the problem. Several examples of structures (piercing or not the interfaces between the fluid layers) satisfying the condition and supporting trapped modes are given.
  • Trapped modes in a multi-layer fluid
    F S Cal, G A S Dias, B M M Pereira, J H Videman
    Quarterly Journal of Mechanics and Applied Mathematics, 2021
    Summary In this article, we study the existence of solutions for the problem of interaction of linear water waves with an array of three-dimensional fixed structures in a density-stratified multi-layer fluid, where in each layer the density is assumed to be constant. Considering time-harmonic small-amplitude motion, we present recursive formulae for the coefficients of the eigenfunctions of the spectral problem associated with the water-wave problem in the absence of obstacles and for the corresponding dispersion relation. We derive a variational and operator formulation for the problem with obstacles and introduce a sufficient condition for the existence of propagating waves trapped in the vicinity of the array of obstacles. We present several (arrays of) structures supporting trapped waves and discuss the possibility of approximating the continuously stratified fluid by a multi-layer model.
  • Lubrication approximation for fluids with shear-dependent viscosity
    Bruno M.M. Pereira, Gonçalo A.S. Dias, Filipe S. Cal, Kumbakonam R. Rajagopal, Juha H. Videman
    Fluids, 2019
    We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing.
  • On the lubrication approximation for a class of viscoelastic fluids
    Filipe S. Cal, Gonçalo A.S. Dias, Bruno M.M. Pereira, Gabriel E. Pires, K.R. Rajagopal, et al.
    International Journal of Non Linear Mechanics, 2016
  • Trapped modes along a periodic array of freely floating obstacles
    Gonçalo A. S. Dias, Juha H. Videman
    Mathematical Methods in the Applied Sciences, 2015
    We consider the coupled problem describing the motion of a linear array of three‐dimensional obstacles floating freely in a homogeneous fluid layer of finite depth. The interaction of time‐harmonic waves with the floating objects is analyzed under the usual assumptions of linear water‐wave theory. Quasi‐periodic boundary conditions and a simplified reduction scheme turn the system into a linear spectral problem for a self‐adjoint operator in Hilbert space. Based upon the operator formulation, we derive a sufficient condition for the nonemptiness of its discrete spectrum. Various examples of obstacles that generate trapped modes are given. Copyright © 2014 John Wiley & Sons, Ltd.
  • Linearised theory for surface and interfacial waves interacting with freely floating bodies in a two-layer fluid
    Filipe S. Cal, Gonçalo A. S. Dias, Serguei A. Nazarov, Juha H. Videman
    Zeitschrift Fur Angewandte Mathematik Und Physik, 2015
  • Trapped modes around freely floating bodies in a two-layer fluid channel
    Filipe S. Cal, Gonçalo A. S. Dias, Juha H. Videman
    Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, 2014
  • Edge waves propagating in a two-layer fluid along a periodic coastline
    F. S. Cal, G. A. S. Dias, B. M. M. Pereira, J. H. Videman
    Journal of Engineering Mathematics, 2014
  • Existence of trapped modes along periodic structures in a two-layer fluid
    F. S. Cal, G. S. A. Dias, J. H. Videman
    Quarterly Journal of Mechanics and Applied Mathematics, 2012
  • Thin-shell wormholes in d-dimensional general relativity: Solutions, properties, and stability
    Gonçalo A. S. Dias, José P. S. Lemos
    Physical Review D Particles Fields Gravitation and Cosmology, 2010
  • Hamiltonian thermodynamics of d -dimensional (d ≥ 4) Reissner-Nordström-anti-de Sitter black holes with spherical, planar, and hyperbolic topology
    Gonçalo A. S. Dias, José P. S. Lemos
    Physical Review D Particles Fields Gravitation and Cosmology, 2009
  • Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes
    Gonçalo A. S. Dias, José P. S. Lemos
    Physical Review D Particles Fields Gravitation and Cosmology, 2008
  • Hamiltonian thermodynamics of three-dimensional dilatonic black holes
    Gonçalo A. S. Dias, José P. S. Lemos
    Physical Review D Particles Fields Gravitation and Cosmology, 2008
  • Charged shells in Lovelock gravity: Hamiltonian treatment and physical implications
    Gonçalo A. S. Dias, Sijie Gao, José P. S. Lemos
    Physical Review D Particles Fields Gravitation and Cosmology, 2007
  • Conformal entropy from horizon states: Solodukhin's method for spherical, toroidal, and hyperbolic black holes in D-dimensional anti-de Sitter spacetimes
    Gonçalo A. S. Dias, José P. S. Lemos
    Physical Review D Particles Fields Gravitation and Cosmology, 2006

RECENT SCHOLAR PUBLICATIONS

  • Trapped Modes Along Periodic Structures Submerged in a Two-Layer Fluid with Free Surface and a Background Steady Flow
    G Dias, B Pereira
    Axioms 14 (11), 846 , 2025
    2025
  • Flow of a Periodic Interfacial Travelling Water Wave: FS Cal, GAS Dias
    FS Cal, GAS Dias
    Water Waves 7 (3), 495-519 , 2025
    2025
  • Trapped Modes Along Periodic Structures Submerged in a Three-Layer Fluid with a Background Steady Flow
    GAS Dias, BMM Pereira
    Computation 13 (8), 176 , 2025
    2025
  • Velocity and energy of periodic travelling interfacial waves between two bounded fluids
    FS Cal, GAS Dias
    Wave Motion 123, 103232 , 2023
    2023
    Citations: 4
  • Wave trapping by freely floating obstacles in a discretely stratified fluid
    FS Cal, GAS Dias, BMM Pereira, JH Videman
    Mathematical Methods in the Applied Sciences, 1-21 , 2023
    2023
    Citations: 1
  • Trapped modes along periodic structures submerged in a two‐layer fluid with background steady flow
    GAS Dias
    Mathematical Methods in the Applied Sciences, 1-26 , 2023
    2023
    Citations: 2
  • Trapped modes in a fluid with three layers topped by a rigid lid
    FS Cal, GAS Dias, BMAM Pereira
    Mathematical Methods in the Applied Sciences 45 (16), 9928-9944 , 2022
    2022
    Citations: 2
  • Trapped modes in a multi-layer fluid
    FS Cal, GAS Dias, BMM Pereira, JH Videman
    The Quarterly Journal of Mechanics and Applied Mathematics 74 (1), 34-54 , 2021
    2021
    Citations: 8
  • Lubrication approximation for fluids with shear-dependent viscosity
    BMM Pereira, GAS Dias, FS Cal, KR Rajagopal, JH Videman
    Fluids 4 (2), 98 , 2019
    2019
    Citations: 8
  • Investigating Beccari’s Claims with New Cartometric Methods
    GAS Dias
    e-Perimetron 13 (3), 141-160 , 2018
    2018
    Citations: 1
  • On the lubrication approximation for a class of viscoelastic fluids
    FS Cal, GAS Dias, BMM Pereira, GE Pires, KR Rajagopal, JH Videman
    International Journal of Non-Linear Mechanics 87, 30-37 , 2016
    2016
    Citations: 5
  • Trapped modes along a periodic array of freely floating obstacles
    GAS Dias, JH Videman
    Mathematical Methods in the Applied Sciences 38 (17), 4038-4051 , 2015
    2015
    Citations: 2
  • Linearised theory for surface and interfacial waves interacting with freely floating bodies in a two-layer fluid
    FS Cal, GAS Dias, SA Nazarov, JH Videman
    Zeitschrift für angewandte Mathematik und Physik 66 (2), 417-432 , 2015
    2015
    Citations: 14
  • Trapped modes around freely floating bodies in a two-layer fluid channel
    FS Cal, GAS Dias, JH Videman
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering … , 2014
    2014
    Citations: 6
  • Edge waves propagating in a two-layer fluid along a periodic coastline
    FS Cal, GAS Dias, BMM Pereira, JH Videman
    Journal of engineering mathematics 85 (1), 1-17 , 2014
    2014
    Citations: 11
  • Trapped modes around freely floating bodies in two-layer fluids
    FS CAL, GAS DIAS, JH VIDEMAN
    Int. J. Numer. Anal. Model. 5, 400 , 2014
    2014
    Citations: 1
  • Wave Interaction with Floating Bodies in a Stratified Multilayered Fluid
    FS Cal, GAS Dias, JH Videman
    Dynamics, Games and Science, 153 , 2013
    2013
    Citations: 1
  • Thin-shell wormholes in -dimensional general relativity: Solutions, properties, and stability
    GAS Dias, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 82 (8), 084023 , 2010
    2010
    Citations: 168
  • Hamiltonian thermodynamics of -dimensional ( ) Reissner-Nordström-anti-de Sitter black holes with spherical, planar, and hyperbolic topology
    GAS Dias, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 79 (4), 044013 , 2009
    2009
    Citations: 17
  • Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes
    GAS Dias, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 78 (8), 084020 , 2008
    2008
    Citations: 7

MOST CITED SCHOLAR PUBLICATIONS

  • Thin-shell wormholes in -dimensional general relativity: Solutions, properties, and stability
    GAS Dias, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 82 (8), 084023 , 2010
    2010
    Citations: 168
  • Conformal entropy from horizon states: Solodukhin’s method for spherical, toroidal, and hyperbolic black holes in -dimensional anti-de Sitter spacetimes
    GAS Dias, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 74 (4), 044024 , 2006
    2006
    Citations: 18
  • Hamiltonian thermodynamics of -dimensional ( ) Reissner-Nordström-anti-de Sitter black holes with spherical, planar, and hyperbolic topology
    GAS Dias, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 79 (4), 044013 , 2009
    2009
    Citations: 17
  • Charged shells in Lovelock gravity: Hamiltonian treatment and physical implications
    GAS Dias, S Gao, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 75 (2), 024030 , 2007
    2007
    Citations: 17
  • Linearised theory for surface and interfacial waves interacting with freely floating bodies in a two-layer fluid
    FS Cal, GAS Dias, SA Nazarov, JH Videman
    Zeitschrift für angewandte Mathematik und Physik 66 (2), 417-432 , 2015
    2015
    Citations: 14
  • Edge waves propagating in a two-layer fluid along a periodic coastline
    FS Cal, GAS Dias, BMM Pereira, JH Videman
    Journal of engineering mathematics 85 (1), 1-17 , 2014
    2014
    Citations: 11
  • Trapped modes in a multi-layer fluid
    FS Cal, GAS Dias, BMM Pereira, JH Videman
    The Quarterly Journal of Mechanics and Applied Mathematics 74 (1), 34-54 , 2021
    2021
    Citations: 8
  • Lubrication approximation for fluids with shear-dependent viscosity
    BMM Pereira, GAS Dias, FS Cal, KR Rajagopal, JH Videman
    Fluids 4 (2), 98 , 2019
    2019
    Citations: 8
  • Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes
    GAS Dias, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 78 (8), 084020 , 2008
    2008
    Citations: 7
  • Trapped modes around freely floating bodies in a two-layer fluid channel
    FS Cal, GAS Dias, JH Videman
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering … , 2014
    2014
    Citations: 6
  • On the lubrication approximation for a class of viscoelastic fluids
    FS Cal, GAS Dias, BMM Pereira, GE Pires, KR Rajagopal, JH Videman
    International Journal of Non-Linear Mechanics 87, 30-37 , 2016
    2016
    Citations: 5
  • Velocity and energy of periodic travelling interfacial waves between two bounded fluids
    FS Cal, GAS Dias
    Wave Motion 123, 103232 , 2023
    2023
    Citations: 4
  • Hamiltonian thermodynamics of three-dimensional dilatonic black holes
    GAS Dias, JPS Lemos
    Physical Review D—Particles, Fields, Gravitation, and Cosmology 78 (4), 044010 , 2008
    2008
    Citations: 3
  • Trapped modes along periodic structures submerged in a two‐layer fluid with background steady flow
    GAS Dias
    Mathematical Methods in the Applied Sciences, 1-26 , 2023
    2023
    Citations: 2
  • Trapped modes in a fluid with three layers topped by a rigid lid
    FS Cal, GAS Dias, BMAM Pereira
    Mathematical Methods in the Applied Sciences 45 (16), 9928-9944 , 2022
    2022
    Citations: 2
  • Trapped modes along a periodic array of freely floating obstacles
    GAS Dias, JH Videman
    Mathematical Methods in the Applied Sciences 38 (17), 4038-4051 , 2015
    2015
    Citations: 2
  • Wave trapping by freely floating obstacles in a discretely stratified fluid
    FS Cal, GAS Dias, BMM Pereira, JH Videman
    Mathematical Methods in the Applied Sciences, 1-21 , 2023
    2023
    Citations: 1
  • Investigating Beccari’s Claims with New Cartometric Methods
    GAS Dias
    e-Perimetron 13 (3), 141-160 , 2018
    2018
    Citations: 1
  • Trapped modes around freely floating bodies in two-layer fluids
    FS CAL, GAS DIAS, JH VIDEMAN
    Int. J. Numer. Anal. Model. 5, 400 , 2014
    2014
    Citations: 1
  • Wave Interaction with Floating Bodies in a Stratified Multilayered Fluid
    FS Cal, GAS Dias, JH Videman
    Dynamics, Games and Science, 153 , 2013
    2013
    Citations: 1