Conservative vector field ≈ Conservative vector field
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Integral Line-of-Sight Guidance and Control of Underactuated Marine Vehicles: Theory, Simulations, and Experiments Open
This paper presents an extensive analysis of the integral line-of-sight (ILOS) guidance method for path-following tasks of underactuated marine vehicles, operating on and below the sea surface. It is shown that due to the embedded integral…
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Explosive Higher-Order Kuramoto Dynamics on Simplicial Complexes Open
The higher-order interactions of complex systems, such as the brain, are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make …
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Integral Line-of-Sight Guidance for Path Following Control of Underwater Snake Robots: Theory and Experiments Open
This paper proposes and experimentally validates a straight line path following controller for underwater snake robots in the presence of constant irrotational currents of unknown direction and magnitude. An integral line-of-sight (LOS) gu…
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A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time Open
A perfect-fluid space-time of dimension n ≥ 4, with (1) irrotational velocity vector field and (2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with an Einstein fiber. Condition (1) is verified whenever …
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Cluster phases and bubbly phase separation in active fluids: Reversal of the Ostwald process Open
It is known that purely repulsive self-propelled colloids can undergo bulk liquid-vapor phase separation. In experiments and large scale simulations, however, more complex steady states are also seen, comprising a dynamic population of den…
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Flow structure beneath rotational water waves with stagnation points Open
The purpose of this work is to explore in detail the structure of the interior flow generated by periodic surface waves on a fluid with constant vorticity. The problem is mapped conformally to a strip and solved numerically using spectral …
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Extended logotropic fluids as unified dark energy models Open
\n We study extended classes of logotropic fluids as unified dark energy models. Under the hypothesis of the Anton–Schmidt scenario, we consider a universe obeying a single fluid model with a logarithmic equation of state. We investigate t…
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New approach to nonrelativistic diffeomorphism invariance and its applications Open
A comprehensive account of a new structured algorithm for obtaining\nnonrelativistic diffeomorphism invariances in both space and spacetime by\ngauging the Galilean symmetry in a generic nonrelativistic field theoretical\nmodel is provided…
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Empirical moments of inertia of axially asymmetric nuclei Open
We extracted empirical moments of inertia, J1, J2, J3, of atomic nuclei with E(4$+\\atop{1}$)/E(2$+\\atop{1}$ ) > 2.7 from experimental 2$+\\atop{g,y}$, energies and electric quadrupole matrix elements, determined from multi- step Coulomb …
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Experimental study of particle trajectories below deep-water surface gravity wave groups Open
Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth belo…
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Non‐hydrostatic, Non‐linear Processes in the Surf Zone Open
In the surf zone, non‐hydrostatic processes are either neglected or estimated using linear wave theory. The recent development of technologies capable of directly measuring the free surface elevation, such as 2‐D lidar scanners, allow for …
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On warped product gradient η-Ricci solitons Open
If the potential vector field of an ?-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a nonlinear second order PDE. In a particular case of irrotational potential vector field we prove that the…
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On the magnetic field evolution time-scale in superconducting neutron star cores Open
We revisit the various approximations employed to study the long-term\nevolution of the magnetic field in neutron star cores and discuss their\nlimitations and possible improvements. A recent controversy on the correct form\nof the inducti…
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Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution Open
Motivated by ongoing experimental efforts to make closed Bose-Einstein\ncondensate (BEC) shells in microgravity environments, this work studies the\nenergy and dynamics of singly quantized vortices on a thin spherical superfluid\nshell, wh…
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Global Regularity for 2d Water Waves with Surface Tension Open
We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a…
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A zonal hybrid approach coupling FNPT with OpenFOAM for modelling wave-structure interactions with action of current Open
This paper presents a hybrid numerical approach, which combines a two-phase Navier- Stokes model (NS) and the fully nonlinear potential theory (FNPT), for modelling wave-structure interaction. The former governs the computational domain ne…
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Extrema of the dynamic pressure in an irrotational regular wave train Open
We prove that in a regular wave train, which propagates at the surface of water in irrotational flow over a flat bed, the maximum and minimum of the dynamic pressure occur at the wave crest and at the wave trough, respectively. This result…
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Waves on a vortex: rays, rings and resonances Open
We study the scattering of surface water waves with irrotational draining vortices. At small depth, this system is a mathematical analogue of a rotating black hole and can be used to mimic some of its peculiar phenomena. Using ray-tracing …
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Liquid vibrations in cylindrical tanks with flexible membranes Open
The objectives of this paper are in studying the liquid vibrations in rigid circular cylindrical shells with internal flexible membranes or covered by membranes. The liquid in the container is supposed to be an ideal and incompressible one…
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Flow pressure evaluation on generic surfaces by robotic volumetric PTV Open
An experimental approach for the measurement of the time-average fluid flow pressure over the surface of generic three-dimensional objects is presented. The method is based on robotic volumetric PTV measurements followed by the integration…
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SINGULAR BOUNDARY METHOD IN A FREE VIBRATION ANALYSIS OF COMPOUND LIQUID-FILLED SHELLS Open
A new numerical approach is proposed to address problems of free liquid vibrations in axisymmetric compound rigid shells using a singular boundary method.The liquid is supposed to be perfect and incompressible, and its flow is irrotational…
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Switching the curl of polarization vectors by an irrotational electric field Open
Ferroelectric vortex domains are of significant interest due to their rich physics and potential applications. Here, we propose the crystallographic, strain, and electric conditions for spontaneous vortex domains and study the influence of…
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Hydrodynamic thermoelectric transport in Corbino geometry Open
Here we study hydrodynamic electron transport in Corbino graphene devices. Due to the irrotational character of the flow, the forces exerted on the electron liquid are expelled from the bulk. We show that in the absence of Galilean invaria…
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Nonlinear Wave–Current Interactions in Shallow Water Open
We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green–Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of s…
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Free vibration analysis of coupled sloshing-flexible membrane system in a liquid container Open
A finite element model is developed to study free vibration of a liquid in a tank of arbitrary geometry with a flexible membrane constraining the liquid free-surface. A variational formulation is initially developed using the Galerkin meth…
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Impact of turbulence and secondary flow on the water surface in partially filled pipes Open
Large eddy simulations (LESs) of turbulent flow in partially filled pipes at various filling degrees are conducted to investigate the response of the water surface to the turbulence and the secondary flow below it. LESs are validated first…
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Vorticity in analogue spacetimes Open
Analogue spacetimes can be used to probe and study physically interesting spacetime geometries by constructing, either theoretically or experimentally, some notion of an effective Lorentzian metric $[g_\mathrm{eff}(g,V,\,\Xi)]_{ab}$. These…
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Solitary flexural–gravity waves in three dimensions Open
The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying K…
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Derrick’s theorem in curved spacetime Open
We extend Derrick's theorem to the case of a generic irrotational curved\nspacetime adopting a strategy similar to the original proof. We show that a\nstatic relativistic star made of real scalar fields is never possible\nregardless of the…
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Capturing the flow beneath water waves Open
Recently, the authors presented two numerical studies for capturing the flow structure beneath water waves (Nachbin and Ribeiro-Junior 2014 Disc. Cont. Dyn. Syst. A 34 , 3135–3153 ( doi:10.3934/dcds.2014.34.3135 ); Ribeiro-Junior et al. 20…