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Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
Implementation of an outlet boundary condition is challenging in the context of the weakly-compressible Smoothed Particle Hydrodynamics method. We perform a systematic numerical study of several of the available techniques for the outlet…
Periodic boundary conditions (PBCs) are a practical necessity in cosmological simulations, but they can also introduce numerical artifacts. We quantified the prevalence of PBC-related artifacts in the IllustrisTNG using dark-matter-deprived…
The isoperimetric problem is one of the oldest in geometry and it consists of finding a surface of minimum area that encloses a given volume $V$. It is particularly important in physics because of its strong relation with stability, and…
3D-0D coupled flow models are widely used across many application fields but remain challenging to solve. Implicit coupling introduces non-local terms, whereas explicit coupling results in only conditionally stable schemes. Furthermore,…
The accurate and efficient simulation of Partial Differential Equations (PDEs) in and around arbitrarily defined geometries is critical for many application domains. Immersed boundary methods (IBMs) alleviate the usually laborious and…
This paper compares Tensor Boundary Conditions (TBCs), which were introduced to model multilayered dielectric structures, with Generalized Sheet Transition Conditions (GSTCs), which have been recently used to model metasurfaces. It shows…
This paper presents a time-domain implementation of the Method of Auxiliary Sources (MAS) combined with the Standard Impedance Boundary Condition (SIBC) for electromagnetic scattering problems involving cylindrical scatterers with finite…
We describe a new approach to derive numerical approximations of boundary conditions for high-order accurate finite-difference approximations. The approach, called the Local Compatibility Boundary Condition (LCBC) method, uses boundary…
Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold…
Physics-based simulation is essential for developing and evaluating robot manipulation policies, particularly in scenarios involving deformable objects and complex contact interactions. However, existing simulators often struggle to balance…
Summation-by-parts (SBP) finite difference methods have several desirable properties for second-order wave equations. They combine the computational efficiency of narrow-stencil finite difference operators with provable stability on…
Bifurcation problems in which periodic boundary conditions (PBC) or Neumann boundary conditions (NBC) are imposed often involve partial differential equations that have Euclidean symmetry. In this case posing the bifurcation problem with…
This work is concerned with the safety controller synthesis of stochastic hybrid systems, in which continuous evolutions are described by stochastic differential equations with both Brownian motions and Poisson processes, and instantaneous…
Discrete transparent boundary conditions (DTBC) and the Perfectly Matched Layers (PML) method for the realization of open boundary conditions in quantum device simulations are compared, based on the stationary and time-dependent…
In this paper, we apply the variational method with the Structural Prescribed Boundary Conditions (SPBC) to prove the existence of periodic and quasi-periodic solutions for planar four-body problem with $m_1=m_3$ and $m_2=m_4$. A path…
We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by…
A theoretical framework is developped leading to a sound derivation of Periodic Boundary Conditions (PBCs) for the analysis of domains smaller then the Unit Cells (UCs), named reduced Unit Cells (rUCs), by exploiting non-orthogonal…
Implementing computational boundary conditions, such as perfectly matched layers PML does have advantages for forwarding modeling of the earth's crust. The mathematical modeling of many physical problems encountered in industrial…
Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be…