相关论文: Self Consistent Expansion for the Molecular Beam E…
A review is provided of our current theoretical understanding of dynamic scaling in nonequilibrium interface growth as, for example, in MBE growth under ultrahigh vacuum deposition conditions.
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
Numerical simulations are essential tools for exploring the dynamic scaling properties of the nonlinear Kadar-Parisi-Zhang (KPZ) equation. Yet the inherent nonlinearity frequently causes numerical divergence within the strong-coupling…
We consider the identification of heterogeneous linear elastic moduli in the context of time-harmonic elastodynamics. This inverse problem is formulated as the minimization of the modified error in constitutive equation (MECE), an…
We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by…
In this paper, we initiate the study of backward doubly stochastic differential equations (BDSDEs, for short) with quadratic growth. The existence, comparison, and stability results for one-dimensional BDSDEs are proved when the generator…
We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the…
Mixture of Experts (MoE) models scale capacity but often suffer from representation collapse and gradient instability. We propose Dynamic Subspace Composition (DSC), a framework that approximates context-dependent weights via a…
Linear theory of the parametric beam instability or the self-amplification of parametric x-ray radiation (PXR) from relativistic electrons in a crystal is considered taking into account finite emittance of the electron beam and absorption…
Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint…
We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a…
In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
A Multi-scale Boltzmann Equation (MBE) is found from the gas-kinetic theory and the direct modeling philosophy as a master equation for complex physical systems of neutral gases across all flow regimes, which locates between the continuum…
The spectra of masses and decay constants for non-strange meson resonances in the energy range 0--2.5 GeV is analyzed. It is known from meson phenomenology that for given quantum numbers these spectra approximately follow linear…
We prove the existence and uniqueness of the complexified Nonlinear Poisson-Boltzmann Equation (nPBE) in a bounded domain in $\mathbb{R}^3$. The nPBE is a model equation in nonlinear electrostatics. The standard convex optimization argument…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
We report the growth of epitaxial LaInO3 on DyScO3(110) substrates by adsorption-controlled plasma-assisted molecular beam epitaxy (PA-MBE). The adsorption-controlled growth was monitored using line-of-sight quadrupole mass spectrometry. In…
{\em NOTE: This paper presented the first attempt to tackle the Kardar-Parisi-Zhang (KPZ) equation using non-perturbative renormalisation group (NPRG) methods. It exploited the most natural and frequently used approximation scheme within…
A fast explicit operator splitting (FEOS) method for the molecular beam epitaxy model has been presented in [Cheng, et al., Fast and stable explicit operator splitting methods for phase-field models, J. Comput. Phys., submitted]. The…