Jerzy Gorecki

On the ground state of the hydrogen molecule–ion H+2 enclosed in hard and soft spherical boxes

Iterative boundary perturbation theory is applied to the hydrogen molecule–ion H+2 enclosed in spheroidal boxes with finite and infinite walls. The mechanical pressure dependence of ground state properties such as the equilibrium bond length, the change of electronic kinetic energy, quadrupole moment, and the vibrational force constant are presented and discussed. For the hard box, our results are compared with those calculated by the variational method and it is clear that in this case the boundary perturbation theory gives a better description of ground state properties. The behavior of the new more realistic model of H+2 at high pressures based on the concept of finite potential wall (soft or padded box) is discussed.

Information processing with structured excitable medium

There are many ways in which a nonlinear chemical medium can be used for information processing. Here we are concerned with an excitable medium and the straightforward method of information coding: a single excitation pulse represents a bit of information and a group of excitations forms a message. Our attention is focused on a specific type of nonhomogeneous medium that has an intentionally introduced geometrical structure of regions characterized by different excitability levels. We show that in information processing applications the geometry plays an equally important role as the dynamics of the medium and allows one to construct devices that perform complex signal processing operations even for a relatively simple kinetics of the reactions involved. In the paper we review a number of published chemical realizations of simple information processing devices like logical gates or memory cells and we show that by combining these devices as building blocks the medium can perform complex operations like for example counting of arriving excitations. We also present a new, simple realizations of chemical signal diode that transmits pulses in one direction only.

Padded-box model for the effect of pressure on helium

The Hartree-Fock method is applied to find the energy of the ground state of the helium atom enclosed in a spherical box with a finite potential wall. The model is used to describe the increase of the electronic kinetic energy of helium gas at high pressures. For pressures less than 25 kbar a small negative potential wall (<-0.1 Hartree) leads to significantly better agreement with experimental results than the widely used hard-box model. An approximate form of a new boundary perturbation method is applied to the enclosed helium atom and very good agreement with the SCF result is found up to pressures of the order of 1 Mbar.

Variational boundary perturbation theory for enclosed quantum systems

The authors propose a new method of solving the Schrodinger equation for a quantum system enclosed in a box with infinite potential walls. The method combines the variational technique with boundary perturbation theory and can be applied to a general non-separable case. When the Schrodinger equation for an enclosed system separates into an ordinary differential equation, the method gives the exact energy and wavefunction. As an application of the method the authors obtain the ground-state energy of the hydrogen atom placed off-centre in a spherical cavity. A generalisation of the variational boundary perturbation technique for finite potential walls is suggested.

On the stochastic correlations in a randomly perturbed chemical front

A stochastic reaction-diffusion equation, which describes the time evolution of a front of concentration in a chemical system characterized by a single active component and influenced by the presence of external noise, is solved within the small noise approximation. The spatial correlations of concentration are studied. The relationship between the spectrum of the evolution operator and the correlation function is discussed and two examples (the trigger wave and the wave between a stable and an unstable state) are discussed.

Iterative boundary perturbation method for enclosed one-dimensional quantum systems

A modification of the boundary perturbation theory of Hull and Julius (1950) is proposed which lends itself to iterative solution. The method may be applied to both finite and infinite box potentials. For enclosed quantum systems described by one-dimensional Schrodinger equations it leads to the exact energy and wavefunction.

Chemical computing with reaction–diffusion processes

Chemical reactions are responsible for information processing in living organisms. It is believed that the basic features of biological computing activity are reflected by a reaction–diffusion medium. We illustrate the ideas of chemical information processing considering the Belousov–Zhabotinsky (BZ) reaction and its photosensitive variant. The computational universality of information processing is demonstrated. For different methods of information coding constructions of the simplest signal processing devices are described. The function performed by a particular device is determined by the geometrical structure of oscillatory (or of excitable) and non-excitable regions of the medium. In a living organism, the brain is created as a self-grown structure of interacting nonlinear elements and reaches its functionality as the result of learning. We discuss whether such a strategy can be adopted for generation of chemical information processing devices. Recent studies have shown that lipid-covered droplets containing solution of reagents of BZ reaction can be transported by a flowing oil. Therefore, structures of droplets can be spontaneously formed at specific non-equilibrium conditions, for example forced by flows in a microfluidic reactor. We describe how to introduce information to a droplet structure, track the information flow inside it and optimize medium evolution to achieve the maximum reliability. Applications of droplet structures for classification tasks are discussed.

Realistic parameters for simple models of the Belousov-Zhabotinsky reaction.

We use experimental results to estimate the values of parameters of simple models describing the time evolution of the Belousov-Zhabotinsky reaction proceeding in droplets surrounded by hydrocarbons. The equations with fitted parameters correctly describe the period of oscillations for a large class of experimental conditions at which the reaction is performed.

Understanding Networks of Computing Chemical Droplet Neurons Based on Information Flow.

In this paper, we present general methods that can be used to explore the information processing potential of a medium composed of oscillating (self-exciting) droplets. Networks of Belousov-Zhabotinsky (BZ) droplets seem especially interesting as chemical reaction-diffusion computers because their time evolution is qualitatively similar to neural network activity. Moreover, such networks can be self-generated in microfluidic reactors. However, it is hard to track and to understand the function performed by a medium composed of droplets due to its complex dynamics. Corresponding to recurrent neural networks, the flow of excitations in a network of droplets is not limited to a single direction and spreads throughout the whole medium. In this work, we analyze the operation performed by droplet systems by monitoring the information flow. This is achieved by measuring mutual information and time delayed mutual information of the discretized time evolution of individual droplets. To link the model with reality, we use experimental results to estimate the parameters of droplet interactions. We exemplarily investigate an evolutionary generated droplet structure that operates as a NOR gate. The presented methods can be applied to networks composed of at least hundreds of droplets.

On the response of simple reactors to regular trains of pulses

Propagating pulses of concentration in an excitable system may carry information because regions of high concentration of a selected reagent may be associated with one logical state, and regions of low concentration with another. Spatially distributed reactors constructed of active (excitable) and passive areas in which reagents diffuse can be applied to transform such information. In this paper we consider a few examples of such reactors (a chemical diode, a cross junction switch) and study their response to a chemical input of high frequency. We demonstrate that the response of a signal processing device may depend on the input frequency.