Related papers: Symplectic bipotentials
This paper proposes that elastic potentials, which may be rigorously formulated using the negative Gibbs free energy or the complementary strain energy density, should be used as the basis for the plastic part of elasto-plastic constitutive…
In this note we apply a 4-fold sum operation to develop an associativity rule for the pairwise symplectic sum. This allows us to show that certain diffeomorphic symplectic $4$-manifolds made out of elliptic surfaces are in fact…
A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy…
A new class of orbital-dependent exchange-correlation (xc) potentials for applications in noncollinear spin-density-functional theory is developed. Starting from the optimized effective potential (OEP) formalism for the exact exchange…
In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…
This paper connects two different approaches to the analysis of Hamiltonian dynamics on non-compact energy hypersurfaces - $b$-symplectic geometry with its singular symplectic form and Floer techniques for tentacular Hamiltonians. More…
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic…
We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can be modeled as a coupled system of some subsystems. Although…
By introducing an integration factor to the differential one-form of contact dynamics, equations of motion are derived variationally, and contact Poisson bracket and contact Lagrangian are formulated. Discrete symplectic integrator, named…
A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…
In this paper, we discuss the non-collapsibility concept and propose a new approach based on Dirichlet process mixtures to estimate the conditional effect of covariates in non-collapsible models. Using synthetic data, we evaluate the…
Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…
We propose a metriplectic reformulation of Lagrangian variational formulations for non-equilibrium thermodynamics. We prove that solutions to these constrained variational principles can be generated by the sum of a classic Poisson bracket…
The basic continuum model for polar fluids is deceptively simple. The free energy integral consists of four terms: The coupling of polarization to an external field, the electrostatic energy of the induced electric field interacting with…
In this work we extend our previously developed formalism of Newtonian multi-fluid hydrodynamics to allow for coupling between the fluids and the electromagnetic and gravitational field. This is achieved within the convective variational…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
We describe a general model for the free energy function for a homogeneous medium of mutually interacting molecules, based on the formalism for a biaxial nematic liquid crystal set out by Katriel {\em et al.} (1986) in an influential paper…
This is the pdf -version of the author's Ph.D. thesis (1995, ULB, Belgium). The notion of symeplectic symmertic space is introduced and studied via Lie theoretical and symplectic geoemetrical methods. The first chapter concerns basic…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
We prove one deformation theoretic extension of the Gromov non-squeezing phenomenon to $lcs$ structures, or locally conformally symplectic structures, which suitably generalize both symplectic and contact structures. We also conjecture an…