Related papers: Improving the quantification of overshooting shock…
We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale $\varepsilon$. Numerical homogenization methods are popular for such problems, because they capture efficiently…
For the past 20 years, our approach to shock capturing in smoothed particle hydrodynamics (SPH) has been to use artificial viscosity and conductivity terms supplemented by switches to control excess dissipation away from shocks (Monaghan…
Noise shaping refers to an analog-to-digital conversion methodology in which quantization error is arranged to lie mostly outside the signal spectrum by means of oversampling and feedback. Recently it has been successfully applied to more…
In shockwave theory, the density, velocity and pressure jumps are derived from the conservation equations. Here, we address the physics of a weak shock the other way around. We first show that the density profile of a weak shockwave in a…
Optical absorption measurements characterize a wide variety of systems from atomic gases to \emph{in-vivo} diagnostics of living organisms. Here we study the potential of non-classical techniques to reduce statistical noise below the…
We analyze the linear stability of a stalled accretion shock in a perfect gas with a parametrized cooling function L ~ rho^{beta-alpha} P^alpha. The instability is dominated by the l=1 mode if the shock radius exceeds 2-3 times the accretor…
The describing function method is a useful tool for the qualitative analysis of limit cycles in the stability analysis of nonlinear systems. This method is inherently approximate; therefore, it should be used for a fast qualitative analysis…
Determining the adsorption isotherms is an issue of significant importance in preparative chromatography. A modern technique for estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides…
We report experimental measurements of inertial waves generated by an oscillating cylinder in a rotating fluid. The two-dimensional wave takes place in a stationary cross-shaped wavepacket. Velocity and vorticity fields in a vertical plane…
Accurate characterization of entropy plays a pivotal role in capturing reversible and irreversible heating in supercapacitors during charging/discharging cycles. However, numerical methods that can faithfully capture entropy variation in…
Adaptive data collection and analysis, where data are being fed back to update the measurement settings, can greatly increase speed, precision, and reliability of the characterization of quantum systems. However, decoherence tends to make…
Numerical discretizations of the Generalized Porous Medium Equation (GPME) with discontinuous coefficients are analyzed with respect to the formation of numerical artifacts. In addition to the degeneracy and self-sharpening of the GPME with…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
We propose a control approach for a class of nonlinear mechanical systems to stabilize the system under study while ensuring that the oscillations of the transient response are reduced. The approach is twofold: (i) we apply our technique…
The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of…
We propose a new technique for a-posteriori diffusion analysis of numerical schemes. The scalar linear advection equation with a broadband signal as initial conditions is numerically solved to simulate a traveling linear wave. A diffusion…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…
Numerical schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence, numerical simulations of wave-like systems lacking proper handling of these…
The sliding mode observer is a useful method for estimating the system state and the unknown disturbance. However, the traditional single-layer observer might still suffer from high pulse when the output measurement is mixed with noise. To…