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Effects of noncommutativity are investigated in planar quantum mechanics in the coordinate representation. Generally these issues are addressed by converting to the momentum space. In the first part of the work we show noncommutative…
Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial…
Space-time coordinates in DSR theories with two invariant scales based on a dispersion relation with an energy independent speed of light are introduced by the demand, that boost and rotation generators are invariant under a transformation…
We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems.…
Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…
Interest in the dynamical arrest leading to a fluid --> solid transition in thermal and athermal systems has led to questions about the nature of these transitions. These jamming transitions may be dependent on the influence of extended…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these…
The dynamics of a spin--1/2 neutral particle possessing electric and magnetic dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a…
This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and…
The stochastic dynamics of orthogonal metal cutting with both regenerative and nonsmooth frictional effects are investigated numerically in this paper. The shortcomings of neglecting nonsmoothness in frictional and stochastic effects in…
Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental…
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
In contrast to the traditional elastodynamic equations, a more comprehensive formulation of one dimensional (1D) elastodynamic equations is given for inhomogeneous media by using the coordinate transformation method. These modified…
Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting…