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We use a conformal mapping technique to study the Laplacian transfer across a rough interface. Natural Dirichlet or Von Neumann boundary condition are simply read by the conformal map. Mixed boundary condition, albeit being more complex can…
Differential equations need boundary conditions (BC's) for their solution. It is commonly acknowledged that differential equations and BC's are representative of independent physical processes, and no correlations between them is required.…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…
We explore in this article the possibilities and limitations of the so-called energy method for analyzing the stability of finite difference approximations to the transport equation with extrapolation numerical boundary conditions at the…
Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface, the network can be rendered…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
An arbitrary order finite difference method for curved boundary domains with Cartesian grid is proposed. The technique handles in a universal manner Dirichlet, Neumann or Robin condition. We introduce the Reconstruction Off-site Data (ROD)…
We present a set of effective outflow/open boundary conditions and an associated algorithm for simulating the dynamics of multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids in domains involving outflows or…
In this paper, we derive differential conditions guaranteeing the orbital stability of nonlinear hybrid limit cycles. These conditions are represented as a series of pointwise linear matrix inequalities (LMI), enabling the search for…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
The "flexible boundary condition" method, introduced by Sinclair and coworkers in the 1970s, remains among the most popular methods for simulating isolated two-dimensional crystalline defects, embedded in an effectively infinite atomistic…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a list of consistency criteria with the geometric setting of…
Navigating cluttered environments is a challenging task for any mobile system. Existing approaches for ground-based mobile systems primarily focus on small wheeled robots, which face minimal constraints with overhanging obstacles and cannot…
Most reinforcement learning(RL)-based methods for drone racing target fixed, obstacle-free tracks, leaving the generalization to unknown, cluttered environments largely unaddressed. This challenge stems from the need to balance racing speed…
We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by…