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We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent bundles, ${\rm…
We develop a bundle picture for the case that the configuration manifold has only a single isotropy type, and give a formula for the reduced symplectic form in this setting. Furthermore, as an application of this bundle picture we consider…
We present a formalism for which a dissipative system is given by a variational principle. The formalism applies to dynamical systems where its trajectory is monotonic. Subsequently, we derive its Lagrangian and Hamiltonian. From the…
Dissipation can be represented in Hamiltonian mechanics in an extended phase space as a symplectic process. The method uses an auxiliary variable which represents the excitation of unresolved dynamics and a Hamiltonian for the interaction…
The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of…
Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of…
In this talk we would like to review recent results on non-singular cosmological models. It has been recently shown that among stiff perfect fluid inhomogeneous spacetimes the absence of singularities is more common than it was expected in…
Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at theoretical level and by molecular dynamic simulations. To understand some of these features…
A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the…
In this paper we study the deformations of bihamiltonian PDEs of hydrodynamic type with one dependent variable. The reason we study such deformations is that the deformed systems maintain an infinite number of commuting integrals of motion…
Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
Reptation theory has been highly successful in explaining the unusual material properties of entangled polymer solutions. It reduces the complex many-body dynamics to a single-polymer description where each polymer is envisaged to be…
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure plays a…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…
Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in…
We derive hydrodynamics of a prototypical one dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients - the hardcore…
The bi-continuum model composed of two interpenetrating and dynamically coupled material continua is analysed as a simplified but relatively accurate way to describe some physical phenomena in crystalline solids. The essential novelty of…
We propose a model to study symmetric binary fluids, based in the mesoscopic molecular simulation technique known as multiparticle collision, where space and state variables are continuous while time is discrete. We include a repulsion rule…