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Non-equilibrium driving systems provide fertile ground for exploring intriguing spontaneous symmetry breaking phenomena. In this study, we report on the intertwined discrete spacetime translational symmetry breaking in a driven-dissipative…

We propose and demonstrate theoretically a method to achieve and design optical nonlinear responses through a light-mediated spatial hybridization of different standard nonlinearities. The mechanism is based on the fact that optical…

We investigate the homogeneity of certain kind of slices of the complete complexification of a proper complex equifocal submanifold in a symmetric space of non-compact type.

Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…

We look into the general aspects of space-time symmetries in presence of torsion, and how the latter is affected by such symmetries. Focusing in particular to space-times which either exhibit maximal symmetry on their own, or could be…

We present a novel numerical solver for the systems of coupled non-linear elliptical differential equations. The solver partitions the computational domain into a set of rectangular pseudo-spectral collocation subdomains and is especially…

Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…

We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal projective transformations. The metrics are manifestly obtained and the projective group properties are determined.…

We are studying Runge-Kutta methods along complex paths of integration from a geometric point of view. Thereby we derive special complex time grids, which applied to the problem of integrating a linear autonomous system of ordinary…

In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving…

For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in P^N is quasi-projective. ----- Pour certaines valeurs des degres des equations, on…

A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied…

Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by…

The procedure for constructing the massive particle surfaces in static space-times is described in detail and the equivalence of the main results with the results of the geodesic approach is demonstrated.

N = 2 supersymmetry in four space-time dimensions is intimately related to hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkahler manifolds. On the…

The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…

We revisit second-order-in-time space-time discretizations of the linear and semilinear wave equations by establishing precise equivalences with first-order-in-time formulations. Focusing on schemes using continuous piecewise-polynomial…

A symplectic, symmetric, second-order scheme is constructed for particle evolution in a time-dependent field with a fixed spatial step. The scheme is implemented in one space dimension and tested, showing excellent adequacy to experiment…

This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always…

We prove local in time Strichartz estimates for the Dirac equation on spherically symmetric manifolds. As an application, we give a result of local well-posedness for some nonlinear models.