arXiv subjects

Jerzy Gorecki

Publications and source records attributed to Jerzy Gorecki.

8 recordsLinked to original sources

arXiv2025

Modeling the time evolution of a camphor rotor perturbed by a stationary camphor source

A self-propelled motion resulting from the dissipation of camphor molecules on the water surface has been attracting scientific attention for more than 200 years. A generally accepted description of the phenomenon includes equations for the object motion coupled with the hydrodynamics of Marangoni flows and the time evolution of camphor surface concentration. The solution of such equations is a numerically complex problem. In recent publications, an alternative approach based on Hamiltonian including the potential term representing Marangoni interactions has been applied to simulate the time evolution of camphor rotors. Such a model represents a significant numerical simplification if compared to the standard description. Here, we comment on the applicability of Hamiltonian approach by applying it to a single camphor rotor perturbed by a camphor disk fixed on the water surface. We demonstrate that in such a case, the approach leads to the results qualitatively different from the experimental ones. Therefore, we doubt in its applicability to describe the time evolution of interacting camphor rotors. We also show that the approximation of the Marangoni forces by a potential gives more realistic results if used together with the equation of motion that includes the hydrodynamic friction. Still, a better agreement with experiments can be obtained by considering an additional equation for the time evolution of camphor surface concentration.

cond-mat.soft↗

arXiv2024

Deformation dynamics of an oil droplet into a crescent shape during intermittent motion

A paraffin droplet containing camphor and oil red O (dye) floating on the water surface shows spontaneous motion and deformation generated by the surface tension gradient around the droplet. We focused on the intermittent motion with a pronounced deformation into a crescent shape observed at specific concentrations of camphor and oil red O. We quantitatively analyzed the time changes in the droplet deformation and investigated the role of the oil red O by measuring the time-dependent paraffin/water interfacial tension with the pendant drop method. The observed effect can be explained by the active role of the oil red O molecules at the paraffin/water interface. The interfacial tension decreases gradually after the interface formation, allowing for the dynamic deformation of the droplet. The combination of the decrease in interfacial tension and the reduction in driving force related to camphor outflow generates intermittent motion with dynamic deformation into a crescent shape.

cond-mat.soft↗

arXiv2020

On the Optimum Geometry and Training Strategy for Chemical Classifiers that Recognize the Shape of a Sphere

In this paper, we continue the discussion on database classifiers constructed with networks of interacting chemical oscillators. In our previous papers we demonstrated that a small, regular network of oscillators can predict if three random numbers in the range $[0,1]$ describe a point located inside a sphere inscribed within the unit cube $[0,1] \times [0,1] \times [0,1]$ with the accuracy exceeding $80 \%$. The parameters of the network were determined using evolutionary optimization. Here we apply the same technique to investigate if the classifier accuracy for this problem can be improved by selecting a specific geometry of interacting oscillators. We also address questions on the optimum size of the training database for evolutionary optimization and on the minimum size of the testing dataset for objective evaluation of classifier accuracy.

nlin.AO↗

arXiv2020

On a simple model that explains inversion of a self-propelled rotor under periodic stop and release operations

We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using such variables as the object location, the surface concentration of active molecules and the hydrodynamic surface flow. The model is applied to simulate the time evolution of a rotor composed of a polygonal plate with camphor pills at its corners. We have qualitatively reproduced results of experiments, in which the inversion of rotational direction under periodic stop-and-release operations was investigated. The model correctly describes the probability of the inversion as a function of the duration of the phase when the rotor is stopped. Moreover, the model allows to introduce the rotor asymmetry unavoidable in real experiments and study its influence on the studied phenomenon. Our numerical simulations have revealed that the probability of the inversion of rotational direction is determined by the competition among the transport of the camphor molecules by the flow, the intrinsic asymmetry of the rotor, and the noise amplitude.

nlin.AO↗

arXiv2019

Bifurcation in the angular velocity of a circular disk propelled by symmetrically distributed camphor pills

We studied rotation of a disk propelled by a number of camphor pills symmetrically distributed at its edge. The disk was put on a water surface so that it could rotate around a vertical axis located at the disk center. In such a system, the driving torque originates from surface tension difference resulting from inhomogeneous surface concentration of camphor molecules released from the pills. Here we investigated the dependence of the stationary angular velocity on the disk radius and on the number of pills. The work extends our previous study on a linear rotor propelled by two camphor pills [Phys. Rev. E, 96, 012609 (2017)]. It was observed that the angular velocity dropped to zero after a critical number of pills was exceeded. Such behavior was confirmed by a numerical model of time evolution of the rotor. The model predicts that, for a fixed friction coefficient, the speed of pills can be accurately represented by a function of the linear number density of pills. We also present bifurcation analysis of the conditions at which the transition between a standing and a rotating disk appears.

nlin.AO↗

arXiv2017

Relationship between the size of camphor-driven rotor and its angular velocity

We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. The disks dissipate camphor molecules. The driving momentum comes from the nonuniformity of surface tension resulting from inhomogeneous surface concentration of camphor molecules around the disks. We investigate the stationary angular velocity as a function of rotor radius $\ell$. For large $\ell$ the angular velocity decreases for increasing $\ell$. At a specific value of $\ell$ the angular velocity reaches its maximum and, for short $\ell$ it rapidly decreases. Such behaviour is confirmed by a simple numerical model. The model also predicts that there is a critical rotor size below which it does not rotate. Within the introduced model we analyze the type of this bifurcation.

nlin.AO↗

arXiv2015

Discrimination of time-dependent inflow properties with a cooperative dynamical system

Many physical, chemical and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here we demonstrate that a system with such properties can be used to discriminate the amplitude or frequency of an external periodic perturbation or input. Numerical simulations performed for a model sigmoidal kinetics illustrate that there exists a narrow range of frequencies and amplitudes within which the system evolves toward significantly different states. Therefore, observation of system evolution should provide information about the characteristics of the perturbation. The discrimination properties for periodic perturbation are generic. They can be observed in various dynamical systems and for different types of periodic perturbation. \end{abstract}

nlin.AO↗

arXiv2011

Vesicle computers: Approximating Voronoi diagram on Voronoi automata

Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata --- finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one excited neighbour; the cell precipitates if a ratio of excited cells in its neighbourhood to its number of neighbours exceed certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate in result of the interaction. Configuration of precipitate represents edges of approximated Voronoi diagram. We discover relation between quality of Voronoi diagram approximation and precipitation threshold, and demonstrate feasibility of our model in approximation Voronoi diagram of arbitrary-shaped objects and a skeleton of a planar shape.

cs.ET↗