Zobrazeno 1 - 10
of 135
pro vyhledávání: '"Haskovec, Jan"'
We propose a mesoscopic modeling framework for optimal transportation networks with biological applications. The network is described in terms of a joint probability measure on the phase space of tensor-valued conductivity and position in physical sp
Externí odkaz:
http://arxiv.org/abs/2401.07922
Autor:
Haskovec, Jan
We study hierarchical properties of optimal transportation networks with biological background. The networks are obtained as minimizers of an energy functional which involves a metabolic cost term of a power-law form with exponent $\gamma>0$. In the
Externí odkaz:
http://arxiv.org/abs/2312.12156
We study self-regulating processes modeling biological transportation networks as presented in \cite{portaro2023}. In particular, we focus on the 1D setting for Dirichlet and Neumann boundary conditions. We prove an existence and uniqueness result un
Externí odkaz:
http://arxiv.org/abs/2307.16436
We prove that asymptotic global consensus is always reached in the Hegselmann-Krause model with finite speed of information propagation $\mathfrak{c}>0$ under minimal (i.e., necessary) assumptions on the influence function. In particular, we assume t
Externí odkaz:
http://arxiv.org/abs/2303.07140
Publikováno v:
Communications on Applied Mathematics and Computation 2023
We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network formation. The numerical method is based on a non-linear finite difference scheme on a uniform Cartesian grid in a 2D domain. The foc
Externí odkaz:
http://arxiv.org/abs/2301.12926
Publikováno v:
Mathematical and Computational Applications 2022
We compare the solutions of two systems of partial differential equations (PDE), seen as two different interpretations of the same model that describes formation of complex biological networks. Both approaches take into account the time evolution of
Externí odkaz:
http://arxiv.org/abs/2209.08292
Publikováno v:
Discrete and Continuous Dynamical Systems, 2023, 43(3&4): 1499-1515
We study self-regulating processes modeling biological transportation networks. Firstly, we write the formal $L^2$-gradient flow for the symmetric tensor valued diffusivity $D$ of a broad class of entropy dissipations associated with a purely diffusi
Externí odkaz:
http://arxiv.org/abs/2207.03542
Autor:
Haskovec, Jan
We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed $\mathfrak{c}>0$. This leads to a system of functional differential equations with state-dependent delay. We prove that, if initially the age
Externí odkaz:
http://arxiv.org/abs/2112.12806
We study an elliptic-parabolic system of partial differential equations describing formation of biological network structures. The model takes into consideration the evolution of the permeability tensor under the influence of a diffusion term, repres
Externí odkaz:
http://arxiv.org/abs/2111.03889
Autor:
Haskovec, Jan
We derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with non-symmetric interaction weights. The condition prescribes smallness of the delay length relative to the decay r
Externí odkaz:
http://arxiv.org/abs/2108.03725