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Spiral waves are ubiquitous signatures of non equilibrium dynamics, appearing across chemical, biological, and active systems. Yet, in many living systems these waves unfold on curved and folded surfaces whose geometry has rarely been…
We study the role of the control parameter triggering nematic order (temperature or concentration) on the dynamical behavior of a system of nanorods under shear. Our study is based on a set of mesoscopic equations of motion for the…
Fractional models and their parameters are sensitive to changes in the intrinsic micro-structures of anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of…
The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
We test methods for the determination of unstable modes in stellar discs: a point collocation scheme in the action sub-space, a scheme based on expansion of the density and potential on the biorthonormal basis, and a finite element method.…
We study the symmetric properties of waveguide modes in presence of gain/losses, anisotropy/bianisotropy, or continuous/discrete rotational symmetry. We provide a comprehensive approach to identity the modal symmetry by constructing a…
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and…
We develop a mesoscopic field theory for the collective nonequilibrium dynamics of multicomponent mixtures of interacting active (i.e., motile) and passive (i.e., nonmotile) colloidal particles with isometric shape in two spatial…
The Newtonian solid-mechanical theory of nodeless spheroidal and torsional of elastic seismic vibrations trapped in the crust of a quaking neutron star is outlined and applied to the modal classification of the quasi-periodic oscillations…
This research thesis presents a novel higher-order spectral element method (SEM) formulated in cylindrical coordinates for analyzing electromagnetic fields in waveguides filled with complex anisotropic media. In this study, we consider a…
We study the flux-flux plots (FFPs) of the Seyfert galaxy SWIFT J2127.4+5654 which was observed simultaneously by XMM-Newton and NuSTAR. The 0.7-2 keV FFPs show a non-linear behaviour, while they are well fitted by a straight line, in the…
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…
We analyze two simple model planar molecules: an ionic molecule with D3 symmetry and a covalent molecule with D6 symmetry. Both symmetries allow the existence of chiral molecular orbitals and normal modes that are coupled to each other in a…
New molecular line observations of the Bok globule Barnard 68 in HCO+ irrefutably confirm the complex pattern of red and blue asymmetric line profiles seen across the face of the cloud in previous observations of CS. The new observations…
Non-periodic folding of periodic crease patterns paves the way to novel nonlinear phenomena that cannot be feasible through periodic folding. This paper focuses on the non-periodic folding of recursive crease patterns generalized from…
Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…
The behaviour of semi-dilute wormlike micelle solutions under vertical vibrations is investigated using classical measurements of the Faraday instability threshold along with two new experiments based on particle imaging velocimetry and…
S8 is the most stable compound of elemental sulfur in solid and liquid phases, at ambient pressure and below 400K. Three crystalline phases of S8 have been clearly identified in this range of thermodynamic parameters, although no…
Emergent crystals are periodic alignment of "emergent particles", i.e., localized collective behavior of atoms or their charges/spins/orbits. These novel states of matter, widely observed in various systems, may deform under mechanical…