Models of Liesegang pattern formation

In this article different mathematical models of the Liesegang phenomenon are exhibited. The main principles of modeling are discussed such as supersaturation theory, sol coagulation and phase separation, which describe the phenomenon using different steps and mechanism beyond the simple reaction scheme. We discuss whether the underlying numerical simulations are able to reproduce several empirical regularities and laws of the corresponding pattern structure. In all cases we highlight the meaning of the initial and boundary conditions in the corresponding mathematical formalism. Above the deterministic ones discrete stochastic approaches are also described. As a main tool for the control of pattern structure the effect of an external electric field is also discussed

A new universal law for the Liesegang pattern formation

Classical regularities describing the Liesegang phenomenon have been observed and extensively studied in laboratory experiments for a long time. These have been verified in the last two decades, both theoretically and using simulations. However, they are only applicable if the observed system is driven by reaction and diffusion. We suggest here a new universal law, which is also valid in the case of various transport dynamics (purely diffusive, purely advective, and diffusion-advection cases). We state that ptot~Xc, where ptot yields the total amount of the precipitate and Xc is the center of gravity. Besides the theoretical derivation experimental and numerical evidence for the universal law is provided. In contrast to the classical regularities, the introduced quantities are continuous functions of time

A szovjet hatalommal szemben : egy litvániai katolikus szamizdat története

In the late 1960s and early 1970s the opposition movement in Lithuania was primarily formed around the Catholic Church, and it had become one of the most organized and successful dissident group in the Soviet Union. The primary mouthpiece of this movement was the illegally published newspaper Chronicle of the Catholic Church in Lithuania, which positioned itself as the defender of human and national rights, as well as the freedom of religion. The Chronicle grants us insight into the events concerning the Catholic Church in the 1970s and 80s and serves as a historical source. The dissident movement against the Soviet Union in Lithuania was helped by the fact that the country managed to keep its ethnic identity (80% of the population was Lithuanian, and there were no large-scale attempts at colonisation, as opposed to Estonia and Latvia), and also religious homogeneity (Lithuanians were mostly Catholic, while the majority of Latvians and Estonians were Lutherans or Orthodox, and only a minority were Catholics)

Systematic front distortion and presence of consecutive fronts in a precipitation system

A new simple reaction-diffusion system is presented focusing on pattern formation phenomena as consecutive precipitation fronts and distortion of the precipitation front.The chemical system investigated here is based on the amphoteric property of aluminum hydroxide and exhibits two unique phenomena. Both the existence of consecutive precipitation fronts and distortion are reported for the first time. The precipitation patterns could be controlled by the pH field, and the distortion of the precipitation front can be practical for microtechnological applications of reaction-diffusion systems

Probability of the emergence of helical precipitation patterns in the wake of reaction-diffusion fronts

Helical and helicoidal precipitation patterns emerging in the wake of reaction-diffusion fronts are studied. In our experiments, these chiral structures arise with well-defined probabilities P_H controlled by conditions such as e.g., the initial concentration of the reagents. We develop a model which describes the observed experimental trends. The results suggest that P_H is determined by a delicate interplay among the time and length scales related to the front and to the unstable precipitation modes and, furthermore, the noise amplitude also plays a quantifiable role.Comment: 7 pages, 5 composite figure

Simulation of reaction-diffusion processes in three dimensions using CUDA

Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research. A general and robust idea is the parallelization of source codes/programs. Recently, the technological development of graphics hardware created a possibility to use desktop video cards to solve numerically intensive problems. We present a powerful parallel computing framework to solve reaction-diffusion equations numerically using the Graphics Processing Units (GPUs) with CUDA. Four different reaction-diffusion problems, (i) diffusion of chemically inert compound, (ii) Turing pattern formation, (iii) phase separation in the wake of a moving diffusion front and (iv) air pollution dispersion were solved, and additionally both the Shared method and the Moving Tiles method were tested. Our results show that parallel implementation achieves typical acceleration values in the order of 5-40 times compared to CPU using a single-threaded implementation on a 2.8 GHz desktop computer.Comment: 8 figures, 5 table