Related papers: Decoupling PDE Computation with Intrinsic or Inert…
Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at…
We extend the theory of topological localised interface modes to systems with damping. The spectral problem is formulated as a root-finding problem for the interface impedance function and Rouch\'e's theorem is used to track the zeros when…
Quite a many electron transport problems in condensed matter physics are analyzed with a quasiparticle Boltzmann equation. For sufficiently slowly varying weak external potentials it can be derived from the basic equations of quantum…
The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. While small quantum systems with discrete energy levels are noiseless and stay coherent forever…
A new phase field model is introduced, which can be viewed as nontrivial generalisation of what is known as the Caginalp model. It involves in particular nonlinear diffusion terms. By formal asymptotic analysis, it is shown that in the…
Inspired by so many possible applications of this class of problems, we seek solution for non-cooperative elliptic systems of two Schrodinger equations. General conditions are assumed under the potentials, which produces convenient…
Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such input-output…
An analytical solution of the equations describing impurity diffusion due to the migration of nonequilibrium impurity interstitial atoms was obtained for the case of the Robin boundary condition on the surface of a semiconductor. The…
Monte Carlo PDE solvers have become increasingly popular for solving heat-related partial differential equations in geometry processing and computer graphics due to their robustness in handling complex geometries. While existing methods can…
We consider the problem of determining an unaccessible part of the boundary of a conductor by mean of thermal measurements. We study a problem of corrosion where a Robin type condition is prescribed on the damaged part and we prove…
This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…
This paper proposes a fully decentralized and recursive approach to online identification of unknown kinematic and dynamic parameters for cooperative manipulation of a rigid body based on commonly used local measurements. To the best of our…
Based on the thermodynamic variation, we rigorously derive the sharp-interface model for solid-state dewetting on a flat substrate in the form of cylindrical symmetry. The governing equations for the model belong to fourth-order geometric…
We consider the vacuum wave function of a free scalar field theory in space partitioned into two regions, with the field obeying Robin conditions (of parameter $\kappa$) on the interface. A direct integration over fields in a subregion is…
In this paper, the use of the Smith-McMillan form in decoupling multiple-input multiple-output system dynamics is analyzed. In short, from a transfer matrix plant model one can obtain a decoupling compensator which leads to a decoupled…
We consider the dunking problem: a solid body at uniform temperature $T_\text{i}$ is placed in a environment characterized by farfield temperature $T_\infty$ and time-independent spatially uniform heat transfer coefficient; we permit…
We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called…
Optimized transmission conditions in domain decomposition methods have been the focus of intensive research efforts over the past decade. Traditionally, transmission conditions are optimized for two subdomain model configurations, and then…
The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have…
We present a flexible discretization technique for computational models of thin tubular networks embedded in a bulk domain, for example a porous medium. These systems occur in the simulation of fluid flow in vascularized biological tissue,…