Results 141 to 150 of about 283,896 (317)
Dual Variational Problems and Action Principles for Chen–Lee and Hopf–Langford Systems
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We describe the construction of dual variational principles and action functionals for nonlinear dynamical systems using a methodology based on the dual Lagrange multiplier formalism and a convex optimization approach, to derive families of dual actions that correspond to the given nonlinear ordinary differential system.
A. Ghose‐Choudhury, Partha Guha
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Diffuse Domain Methods with Dirichlet Boundary Conditions
The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates the problem on a larger, simple domain where the complex geometry is represented by a smooth phase-field function.
Benfield, Luke, Dedner, Andreas
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Mean field games of controls with Dirichlet boundary conditions
ESAIM: Control, Optimisation and Calculus of VariationsIn this paper, we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a mean-field game of controls setting, that is in which the dynamics of each agent is affected not only by the average position of the rest of the agents but also by their average optimal choice.
Mattia Bongini, Francesco Salvarani
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Asymptotic Analysis of the Static Bidomain Model for Pulsed Field Cardiac Ablation
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT Cardiac arrhythmias are caused by faulty electrical signals in the heart, which lead to chaotic wave propagation and impaired cardiac function. This work focuses on a non‐thermal ablation technique based on electroporation (EP), a promising method for treating arrhythmias, called pulsed field ablation (PFA).
Annabelle Collin +2 more
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Parametric mean curvature evolution with a Dirichlet boundary condition.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1995 Let \(\Omega\) be the unit disc in \(\mathbb{R}^ 2\), \(u_ 0 : \Omega \to \mathbb{R}^ 3\). We investigate the problem of finding a family of maps \(v(.,t) : \Omega \to \mathbb{R}^ 3\), \(t \geq 0\) such that \[ v_ t = g^{ij} v_{x_ i x_ j} \text{ in }\Omega \times (0,\infty),\quad v = u_ 0 \text{ on }\partial \Omega \times (0,\infty), \quad v(0) = u_ 0 \
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The article examines a boundary‐value problem in a bounded domain Ωε$$ {\Omega}_{\varepsilon } $$ consisting of perforated and imperforate regions, with Neumann conditions prescribed at the boundaries of the perforations. Assuming the porous medium has symmetric, periodic structure with a small period ε$$ \varepsilon $$, we analyze the limit ...
Taras Melnyk
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Applied SciencesIn the numerical simulation of composite material models, it is often necessary to recover boundary values of the solution to parabolic problems from integral constraints.
Miglena N. Koleva, Lubin G. Vulkov
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Duality for Evolutionary Equations With Applications to Null Controllability
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We study evolutionary equations in exponentially weighted L2$$ {\mathrm{L}}^2 $$‐spaces as introduced by Picard in 2009. First, for a given evolutionary equation, we explicitly describe the ν$$ \nu $$‐adjoint system, which turns out to describe a system backwards in time. We prove well‐posedness for the ν$$ \nu $$‐adjoint system. We then apply
Andreas Buchinger, Christian Seifert
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Local Search and the Evolution of World Models
Topics in Cognitive Science, EarlyView., 2023 Abstract An open question regarding how people develop their models of the world is how new candidates are generated for consideration out of infinitely many possibilities. We discuss the role that evolutionary mechanisms play in this process. Specifically, we argue that when it comes to developing a global world model, innovation is necessarily ...
Neil R. Bramley +3 more
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Isogeometric solution of Helmholtz equation with Dirichlet boundary condition: numerical experiences [PDF]
, 2020 Victoria Hernández Mederos +4 more
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