相关论文: Convergence Properties for the Physarum Solver
Physarum Polycephalum is a slime mold that can solve shortest path problems. A mathematical model based on Physarum's behavior, known as the Physarum Directed Dynamics, can solve positive linear programs. In this paper, we present a family…
In this paper we study dynamics inspired by Physarum polycephalum (a slime mold) for solving linear programs [NTY00, IJNT11, JZ12]. These dynamics are arrived at by a local and mechanistic interpretation of the inner workings of the slime…
Physarum polycephalum inspired algorithm (PPA), also known as the Physarum Solver, has attracted great attention. By modelling real-world problems into a graph with network flow and adopting proper equations to calculate the distance…
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime…
Optimization of fluid transport in the slime mold Physarum polycephalum has been the subject of several modeling efforts in recent literature. Existing models assume that the tube adaptation mechanism in P. polycephalum's tubular network is…
Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in \mathbb{Z}^n$. We show under fairly general conditions that the non-uniform Physarum dynamics \[ \dot{x}_e = a_e(x,t) \left(|q_e| - x_e\right) \] converges to the…
A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…
A plasmodium of Physarum polycephalum is a very large cell visible by unaided eye. The plasmodium is capable for distributed sensing, parallel information processing, and decentralized optimization. It is an ideal substrate for future and…
The Physarum network expands or retracts in response to environmental stimuli, demonstrating an intelligent adaptive capability to locate optimal paths for nutrient transport. The underlying physical mechanism governing this intelligence…
The popular Physarum-inspired Algorithms (PAs) have the potential to solve challenging network optimization problems. However, the existing researches on PAs are still immature and far from being fully recognized. A major reason is that…
We present two results on slime mold computations. In wet-lab experiments (Nature'00) by Nakagaki et al. the slime mold Physarum polycephalum demonstrated its ability to solve shortest path problems. Biologists proposed a mathematical…
Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient…
The directed Physarum dynamics is known to solve positive linear programs: minimize $c^T x$ subject to $Ax = b$ and $x \ge 0$ for a positive cost vector $c$. The directed Physarum dynamics evolves a positive vector $x$ according to the…
Inverse problems of electric conductivity are studied that arise in the design of spherical shielding or cloaking shells and other functional devices used to control DC electric fields. The shells are considered consisting of a finite…
Many steady-state transport problems in condensed matter physics can be reduced to a set of coupled diffusion equations. This is true in particular when relaxation processes are sufficiently fast that the system is in the diffusive…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
Plasmodium of Physarum polycephalum is a single cell visible by unaided eye, which spans sources of nutrients with its protoplasmic network. In a very simple experimental setup we recorded electric potential of the propagating plasmodium.…
In many cases the correct theoretical description of flexoelectricity requires the consideration of the finite size of a body and is reduced to the solution of boundary problems for partial differential equations. Generally speaking, in…
We experimentally derived a unique one-to-one mapping between a range of selected bioactive chemicals and patterns of oscillations of the slime mould's extacellular electrical potential.
In a hybrid plasma solver (particle ions, fluid mass-less electrons) regions of vacuum, or very low charge density, can cause problems since the evaluation of the electric field involves division by charge density. This causes large…