Related papers: A geometrical view of scalar modulation instabilit…
Recent numerical results show that if a scalar is mixed by periodically forced turbulence, the average mixing rate is directly affected for forcing frequencies small compared to the integral turbulence frequency. We elucidate this by an…
We vary the time-frequency mode structure of ultrafast pulse-pumped modulational instability (MI) twin beams in an argon-filled hollow-core kagom\'e-style PCF by adjusting the pressure, pump pulse chirp, fiber length and parametric gain.…
The linear instability of thin, vertically-isothermal Keplerian discs, under the influence of axial magnetic field is investigated. Solutions of the stability problem are found explicitly by asymptotic expansions in the small aspect ratio…
We introduce the conformally-invariant scalar product, originally devised for radiation fields, to the study of the modes of optical resonators. This scalar product allows one to normalize and compare resonant modes using their…
Voltage stability in modern power systems involves coupled dynamics across multiple time scales. Conventional methods based on time-scale separation or static stability margins may overlook instabilities caused by the coupling of slow and…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles…
This paper explores the modal analysis of power systems with high Converter-Interfaced Generation (CIG) penetration utilizing an impedance-based modeling approach. Traditional modal analysis based on the state-space model (MASS) requires…
The Vertical Shear Instability is one of two known mechanisms potentially active in the so-called dead zones of protoplanetary accretion disks. A recent analysis indicates that a subset of unstable modes shows unbounded growth - both as…
In this paper we introduce a model which provides a new approach to the phenomenon of stochastic resonance. It is based on the study of the properties of the stationary distribution of the underlying stochastic process. We derive the…
A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry -…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
It is shown, that diffusion of saturated gain (e.g. diffusion of population inversion in lasers) causes, and/or enhances a modulational instability of generated light field. In case of a subcritical system (e.g. a laser with saturable…
Based on the modern understanding of MHD turbulence theory, we propose a new method for measuring the spectral properties of magnetic turbulence by synchrotron polarization gradient analysis. Using synthetic polarization observational data,…
Using the hierarchy of scales between the mass, $M$, and the width, $\Gamma$, of a heavy, unstable particle we construct an effective theory that allows calculations for resonant processes to be systematically expanded in powers of the…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
This paper studies the robustness of large-scale interconnected systems with respect to external disturbances, focussing on their scalability properties. Specifically, a notion of scalability is introduced that asks for these robustness…
In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…
Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing…