29 citations · 203 across the 30 of their papers we have counts for
33 papers
Contact Geometry of Relativistic Particle Motion
Begum Atesli, Ogul Esen, Michal Pavelka
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamic…
Conformal and Contact Kinetic Dynamics and Their Geometrization
Oğul Esen, Ayten Gezici, Miroslav Grmela +3
We propose a conformal generalization of the reversible Vlasov equation of kinetic plasma dynamics, called conformal kinetic theory. In order to arrive at this formalism, we start…
Direct Poisson neural networks: Learning non-symplectic mechanical systems
Martin Šípka, Michal Pavelka, Oğul Esen +1
In this paper, we present neural networks learning mechanical systems that are both symplectic (for instance particle mechanics) and non-symplectic (for instance rotating rigid bod…
A Discrete Hamilton--Jacobi Theory for Contact Hamiltonian Dynamics
Oğul Esen, Cristina Sardón, Marcin Zajac
In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geo…
On Locally Conformally Cosymplectic Hamiltonian Dynamics and Hamilton-Jacobi Theory
Begüm Ateşli, Oğul Esen, Manuel de León +1
Cosymplectic geometry has been proven to be a very useful geometric background to describe time-dependent Hamiltonian dynamics. In this work, we address the globalization problem o…
On the role of geometry in statistical mechanics and thermodynamics II: Thermodynamic perspective
Ogul Esen, Miroslav Grmela, Michal Pavelka
The General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provides structure of mesoscopic multiscale dynamics that guarantees emergence of equilibrium st…
On the role of geometry in statistical mechanics and thermodynamics I: Geometric perspective
Ogul Esen, Miroslav Grmela, Michal Pavelka
This paper contains a fully geometric formulation of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). Although GENERIC, which is the sum of Hami…
Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
O. Esen, M. de León, M. Lainz +2
In this survey, we review the classical Hamilton Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton Jacobi equation for differen…
Cohomologies and generalized derivation extensions of -Lie algebras
B. Ateşli, O. Esen, S. Sütlü
A cohomology theory, associated to a -Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generali…
-flows Generated by the Curl of a Vector Potential \& Maurer-Cartan Equations
Oğul Esen, Partha Guha, Hasan Gümral
We examine flows admitting vector identity for a multiplier and a potential field $\mathbf{…
Bicocycle Double Cross Constructions
O. Esen, P. Guha, S. Sütlü
We introduce the notion of a bicocycle double cross product (resp. sum) Lie group (resp. Lie algebra), and a bicocycle double cross product bialgebra, generalizing the unified prod…
Tulczyjew's Triplet for Lie Groups III : Higher Order Dynamics and Reductions for Iterated Bundles
Oğul Esen, Hasan Gümral, Serkan Sütlü
Given a Lie group , we elaborate the dynamics on and , which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space , which…
Tulczyjew's Triplet with an Ehresmann connection I: Trivialization and Reduction
Oğul Esen, Mahmut Kudeyt, Serkan Sütlü
We study the trivialization and the reduction of the Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus obtain trivializations…
Cauchy data space and multisymplectic formulation of conformal classical field theories
Ogul Esen, Manuel de León, Cristina Sardón +1
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description…
The globalization problem of the Hamilton-DeDonder-Weyl equations on a local -symplectic framework
Oğul Esen, Manuel de León, Cristina Sardón +1
In this paper we aim at addressing the globalization problem of Hamilton-DeDonder-Weyl equations on a local -symplectic framework and we introduce the notion of {\it locally con…
Hamilton-Jacobi Formalism on Locally Conformally Symplectic Manifolds
Oğul Esen, Manuel de León, Cristina Sardón +1
In this article we provide a Hamilton-Jacobi formalism in locally conformally symplectic manifolds. Our interest in the Hamilton-Jacobi theory comes from the suitability of this th…
Reductions of Topologically Massive Gravity II: First Order Realizations of Second Order Lagrangians
Filiz Çağatay Uçgun, Oğul Esen, Hasan Gümral
Second order degenerate Clèment and Sarıoğlu-Tekin Lagrangians are casted into forms of various first order Lagrangians. Hamiltonian analysis of these equivalent formalisms are per…
On the quest for generalized Hamiltonian descriptions of -flows generated by curl of a vector potential
Oğul Esen, Partha Guha
We study Hamiltonian analysis of three-dimensional advection flow of incompressible nature assuming that dyna…
Multiscale thermodynamics of charged mixtures
Petr Vagner, Michal Pavelka, Ogul Esen
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (revers…
De Donder Form for Second Order Gravity
Jędrzej Śniatycki, Oğul Esen
We show that the De Donder form for second order gravity, defined in terms of Ostrogradski's version of the Legendre transformation applied to all independent variables, is globall…
A Hamilton-Jacobi formalism for higher order implicit systems
O. Esen, M. de León, C. Sardón
In this paper, we present a generalization of a Hamilton--Jacobi theory to higher order implicit differential equations. We propose two different backgrounds to deal with higher or…
Reduction of a Hamilton-Jacobi equation for nonholonomic systems
Oğul Esen, Manuel de León, Víctor Manuel Jiménez Morales +1
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generali…
A Hamilton-Jacobi theory for implicit differential systems
O. Esen, M. de León, C. Sardón
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, descr…
Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians
Filiz Çağatay-Uçgun, Oğul Esen, Hasan Gümral
We study the Hamiltonian formalisms of the second order degenerate Clèment and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed while arriving at the…