Related papers: Analytic formulas for the D-mode Robinson instabil…
Generalizing ideas of MacKay, and MacKay and Saffman, a necessary condition for the presence of high-frequency ( i.e., not modulational) instabilities of small-amplitude periodic solutions of Hamiltonian partial differential equations is…
In this article, we study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Repetitive operations are widely conducted by automatic machines in industry. Periodic disturbances induced by the repetitive operations must be compensated to achieve precise functioning. In this paper, a periodic-disturbance observer…
A disturbance-aware predictive control policy is proposed for DC-AC power inverters with the receding horizon optimization approach. First, a discrete event-driven hybrid automaton model has been constructed for the nonlinear inverter…
A complete calculation of the ${\cal O}(\alpha_s^4)$ perturbative QCD corrections to the hadronic decay width of the $Z$-boson has recently been performed by Baikov et al.[1]. In their analysis, Baikov et al. relied on the conventional…
Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the…
Recently a mechanism of storage ring operation based on the steady-state microbunching has been proposed and investigated, which contains a laser cavity modulator providing the longitudinal focusing for the circulating microbunches. In this…
We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…
Chaotic mixing in a closed vessel is studied experimentally and numerically in different 2-D flow configurations. For a purely hyperbolic phase space, it is well-known that concentration fluctuations converge to an eigenmode of the…
The ATLAS and CMS collaborations discovered a new boson particle. If the new boson is the Higgs boson, the diphoton signal strength is 1.5 - 1.8 times larger than the Standard Model (SM) prediction, while the WW and ZZ signal strengths are…
This chapter deals with the stabilization of a class of linear time-varying parabolic partial differential equations employing receding horizon control (RHC). Here, RHC is finite-dimensional, i.e., it enters as a time-depending linear…
A linear time-invariant dissipative Hamiltonian (DH) system x' = (J-R)Q x, with a skew-Hermitian J, an Hermitian positive semi-definite R, and an Hermitian positive definite Q, is always Lyapunov stable and under weak further conditions…
Storage ring-based steady-state microbunching (SSMB) is a promising approach for generating high-average-power coherent radiation, while the instabilities driven by coherent undulator radiation in the laser modulator (LM) is important for…
Magnetohydrodynamic simulations have shown that a non-unique critical Lundquist number $S_c$ exists, hovering around $S_c \sim 10^4$, above which threshold Sweet-Parker type stationary reconnecting configurations become unstable to a fast…
Smoothed Particle Hydrodynamics (SPH) is plagued by the phenomenon of tensile instability, which is the occurrence of short wavelength zero energy modes resulting in unphysical clustering of particles. The root cause of the instability is…
This paper presents a method to stabilise oscillations occurring in a mixed convective flow in a nearly hemispherical cavity, using actuation based on the receptivity map of the unstable mode. This configuration models the continuous…
We introduce a discrete linear lossy system with an embedded "hot spot" (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective…
We study a nonlocal Poisson problem with discontinuous source term and analyze how the regularity of the integral kernel determines the discontinuity structure of the corresponding solution. Under general assumptions on compactly supported…
The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced "chaotic"…