arXiv subjects

Filip Moučka

Publications and source records attributed to Filip Moučka.

5 recordsLinked to original sources

arXiv2026

Courant algebroid lifts and curved Courant algebroids

We introduce the Courant algebroid lift, a new construction that takes a Courant algebroid together with a vector bundle connection and produces, when the connection is flat in the image of the anchor, a Courant algebroid. In general, this lift produces a Courant-like structure that we call a curved Courant algebroid. We start by establishing a hierarchy of Courant algebroid properties and their associated structures. In this setting, we introduce curved Courant algebroids, which we show to be related to connections with torsion and curved differential graded Lie algebras. We use this to provide a classification of exact curved Courant algebroids. We show that the Courant algebroid lift of an exact Courant algebroid yields a natural link between the Patterson-Walker metric and generalized geometry. By lifting non-exact Courant algebroids, we establish a relation of these lifts to Lie algebras, Poisson and special complex geometry. Finally, we show that Courant algebroid lifts provide a large class of examples of Courant algebroid actions.

math.DG↗

arXiv2026

Symmetric Cartan calculus, the Patterson-Walker metric and Killing vector fields

We develop symmetric Cartan calculus, an analogue of classical Cartan calculus for symmetric differential forms. We first show that the analogue of the exterior derivative, the symmetric derivative, is not unique and its different choices are parametrized by torsion-free affine connections. We use a choice of symmetric derivative to generate the symmetric Lie derivative and the symmetric bracket, and give geometric interpretations of all of them. By proving the structural identities and describing the role of affine morphisms, we reveal an unexpected link of symmetric Cartan calculus with the Patterson-Walker metric, which we recast as a direct analogue of the canonical symplectic form on the cotangent bundle. We show that, in the light of the Patterson-Walker metric, symmetric Cartan calculus becomes a complete analogue of classical Cartan calculus. In this analogy, its Killing vector fields play a central role.

math.DG↗

arXiv2026

Symmetric Poisson geometry, totally geodesic foliations and Jacobi-Jordan algebras

We introduce symmetric Poisson structures as pairs consisting of a symmetric bivector field and a torsion-free connection satisfying an integrability condition analogous to that in usual Poisson geometry. Equivalent conditions in Poisson geometry have inequivalent analogues in symmetric Poisson geometry and we distinguish between symmetric and strong symmetric Poisson structures. We prove that symmetric Poisson structures correspond to locally geodesically invariant distributions together with a characteristic metric, whereas strong symmetric Poisson structures correspond to totally geodesic foliations together with a leaf metric and a leaf connection. We introduce, using the Patterson-Walker metric, a dynamics on the cotangent bundle and show its connection to symmetric Poisson geometry, the parallel transport equation and the Newtonian equation for conservative systems. Finally, we prove that linear symmetric Poisson structures are in correspondence with Jacobi-Jordan algebras, whereas strong symmetric correspond to those that are moreover associative.

math.DG↗

arXiv2025

Anomalous double-layer restructuring in water-in-salt electrolytes at graphitic interfaces governs capacitance

The structure and thickness of the electrical double layer (EDL) at carbon electrodes strongly influence electrochemical performance, yet remain poorly understood in super-concentrated aqueous electrolytes. Here we combine classical and quantum-mechanical molecular dynamics simulations to resolve the interfacial organisation of aqueous LiCl from dilute to water-in-salt (WiS) (1--$20~\mathrm{mol~kg^{-1}}$) concentrations at graphitic electrodes, and compare with electrochemical differential-capacitance measurements from which the potential of zero charge (PZC) is obtained. We uncover a concentration-driven restructuring of the EDL: below $6~\mathrm{mol~kg^{-1}}$, solvated Li$^+$ dominates the outer Helmholtz plane (OHP), but at higher concentrations co-adsorption of Cl$^-$ through solvent-separated ion pairs enforces a near 1:1 Li:Cl ratio at the interface. This transition expands the effective EDL thickness, redistributes the interfacial potential drop, and drives a decrease in the PZC, matching the trend inferred from differential-capacitance measurements on electrolyte-graphite interfaces. Capacitance calculations reveal that while both EDL and quantum contributions vary strongly with concentration, their opposing trends make the total capacitance appear nearly constant for pristine few-layer graphite; for electrodes with smaller quantum capacitance, however, the concentration dependence of the EDL capacitance would be directly reflected in the total capacitance. Solvent-separated ion pairing is identified as the key driver of anomalous EDL behaviour in LiCl WiS electrolytes, establishing design considerations for tuning interfacial capacitance and stability in next-generation aqueous energy-storage systems.

physics.chem-ph↗

arXiv2016

Recent Progress in Molecular Simulation of Aqueous Electrolytes: Force Fields, Chemical Potentials and Solubility

Although aqueous electrolytes are among the most important solutions, the molecular simulation of their intertwined properties of chemical potentials, solubility and activity coefficients has remained a challenging problem, and has attracted considerable recent interest. In this perspectives review, we focus on the simplest case of aqueous sodium chloride at ambient conditions and discuss the two main factors that have impeded progress. The first is lack of consensus with respect to the appropriate methodology for force field (FF) development. We examine how most commonly used FFs have been developed, and emphasize the importance of distinguishing between "Training Set Properties" used to fit the FF parameters, and "Test Set Properties", which are pure predictions of additional properties. The second is disagreement among solubility results obtained, even using identical FFs and thermodynamic conditions. Solubility calculations have been approached using both thermodynamic--based methods and direct molecular dynamics--based methods implementing coexisting solution and solid phases. Although convergence has been very recently achieved among results based on the former approach, there is as yet no general agreement with simulation results based on the latter methodology. We also propose a new method to directly calculate the electrolyte standard chemical potential in the Henry-Law ideality model. We conclude by making recommendations for calculating solubility, chemical potentials and activity coefficients, and outline a potential path for future progress.

cond-mat.soft↗