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Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…
In the direct approach to continua in reduced space dimensions, a thin shell is described as a mathematical surface in three-dimensional space. An exploratory kinematic study of such surfaces could be very valuable, especially if conducted…
The capacity to precisely edit genomes has outpaced our ability to predict the consequences. A cell can be genetically perfect and therapeutically useless: edited exactly as intended, yet unstable, drifting toward unintended fates, or…
The influence od space-time curvature on quantum matter which can be theoretically described by covariant wave equations has not been experimentally established yet. In this paper we analyse in detail the suitability of the Ramsey atom beam…
In this work we investigate the finite-size effects on the phase structure of Walecka model within the framework of generalized Zeta-function, focusing on the influence of temperature as well as the number and length of compactified spatial…
Recently, it has been shown that in graded systems, thermal rectification (TR) effect may remain in the thermodynamical limit. Here, by taking the one-dimensional rotor lattice as an illustrating model, we investigate how the graded…
We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…
We reveal a correspondence between temperature and integrability-breaking in classical and quantum many-body systems through the lens of geometry and adiabatic transformations. Decreasing the temperature, obtained in a standard way through…
Focus of the chapter is on the theoretical approaches aimed to analyze thermoelectric properties at the nanoscale. We discuss several relevant theoretical approaches for different set-ups of nano-devices providing estimations of the…
Motivated by recent interest concerning "puncture repair" in the conformal geometry of compact Riemannian manifolds, a brief exposition on generalisation to the setting of quasiconformal mappings on certain metric measure spaces is…
Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on…
In this paper, we analyze the effect of geometrical constraint on the conformational properties of an infinitely long linear semiflexible polymer chain confined in-between two constraints under good solvent condition in two dimensions. The…
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 Hamiltonian mechanics and gradient dynamics, is a framework…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
We present the formalism of phenomenological thermodynamics in terms of the even-dimensional symplectic geometry, and argue that it catches its geometric essence in a more profound and clearer way than the popular odd-dimensional contact…
The Article demonstrates the spontaneous symmetry breaking of isotropic homogeneous elastic medium in form of transition from Euclidean to Riemann-Cartan internal geometry of medium. The deformation of elastic medium without defects is…
The large-scale structure of the Universe is well approximated by the Friedmann equations, parametrized by several energy densities which can be observationally inferred. A natural question to ask is: How different would the Universe be if…
We investigate the thermodynamic and observational implications for the charged torus-like black holes, a class of solutions distinct from the classical Schwarzschild black holes. We explicitly derive the fundamental thermodynamic…
The response of a pair of differently polarized antennas is determined by their polarization states AND a phase between them which has a geometric part which becomes discontinuous at singular points in the parameter space. Such phase…
A new geometrically exact micro-structured model is constructed using a generalisation of the notion of Riemann-Cartan manifolds and fibre bundle theory of rank 3. This model is based around the concept of two different length scales: a…