Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

Truth, laws and the progress of science

In this paper I analyze the difficult question of the truth of mature scientific theories by tackling the problem of the truth of laws. After introducing the main philosophical positions in the field of scientific realism, I discuss and then counter the two main arguments against realism, namely the pessimistic meta-induction and the abstract and idealized character of scientific laws. I conclude by defending the view that well-confirmed physical theories are true only relatively to certain values of the variables that appear in the laws.

Conservation laws for non-potential operators

The aim of this work is to study the conservation laws of continuous means mechanics and also to extend the Hamiltonian method for these kind of systems in order to valid for non-potential operators through variational approach. Besides illustrating with various examples of mechanical applications we also introduce in this work the new technique in order to treat such problems as the non-potential problem.

Constitutive laws for strong geometric non-linearity

This paper is divided into two different parts. The first one provides a brief introduction to the fractal geometry with some simple illustrations in fluid mechanics. We thought it would be helpful to introduce the reader into this relatively new approach to mechanics that has not been sufficiently explored by engineers yet. Although in fluid mechanics, mainly in problems of percolation and binary flows, the use of fractals has gained some attention, the same is not true for solid mechanics, from the best of our knowledge. The second part deals with the mechanical behavior of thin wires subjected to very large deformations. It is shown that starting to a plausible conjecture it is possible to find global constitutive equations correlating geometrical end energy variables with the fractal dimension of the solid subjected to large deformations. It is pointed out the need to complement the present proposal with experimental work.

Psychophysical estimation of acid intensity and determination of sweet-acid interaction in a fish paste containing glycerol

In a fish paste made with cooked Brazilian flathead (Percophis brasiliensis), glycerol (17%), sodium chloride (1.5%) and potassium sorbate (0.1%) the following acid percentages: 0.2; 0.4; 0.6; 0.8, 1 and 1.5% w/w were incorporated to determine the relationship between added acetic acid and the sensorially perceived intensity, and the effects of the combination of sweet-acid tastes. Tests for paired comparison, ranking and structured verbal scales for sweet and acid attributes and psychophysical test were carried out. There was a perceptible difference among samples for differences of 0.4 units of acid concentration. Samples indicated as sweeter by 89.47% of the judges were those containing a lesser acid concentration. A reduction in glycerol sweetness when increasing acid levels was observed. Acetic acid reduced the sweetness of glycerol and inversely glycerol reduced the acidity of acetic acid. The data obtained with the magnitude estimation test agree with Steven's law.

Food production in solidarity economy: an issue that goes beyond laws

Abstract Food production within the context of solidarity economy is an alternative way to offer employment and income for a significant part of the Brazilian population. The purpose of this study was to carry out a business diagnosis in order to evaluate the facilities, the production process and hygiene practices of seven solidarity economy enterprises located in the city of Novo Hamburgo, Southern Brazil, that work with food production and sales. Visits took place at the enterprises and a check-list was used to record data. Although food production happens in places with space and setting restrictions, it guarantees distinctive foods with aggregate value, where handlers follow the whole process, from raw materials selection to sales. Basic hygiene principles are followed, as they guarantee the production of food with quality, which contributes towards income generation for participating families. Specific laws that apply to the characteristics and needs of small-scale food production must be written in order to regulate solidarity economy enterprises.

Mr. Giles' speech, delivered in the Senate of the United States, on Thursday, 24th November, 1808, on the resolution of Mr. Hillhouse, to repeal the embargo laws. --

Caption title.

By-laws of the municipal council of the United Counties of Lincoln and Welland, 1852

By-laws included are numbers 31-34 and deal with school issues, raising funds for the municipality, payment of fees, and remuneration to the sheriff of the municipality.

By Laws of the Corporation of the Town of Welland, 1878 [fragment]

The fragment appears to be part of a larger group of bylaws for the Town of Welland, 1878. The fragment includes bylaws Cap. I and Cap. II. Cap. I is a bylaw appointing auditors for the town for the year 1878. Due to paper loss only a portion of the title of the Cap. II bylaw is extent but appears to be a bylaw appointing a Hey…….trustee for the town. Welland was incorporated in 1858 as a town and became a city in 1917.

Mr. Giles' speech, delivered in the Senate of the United States, on Thursday, 24th November, 1808, on the resolution of Mr. Hillhouse, to repeal the embargo laws

Printed by Pool and Palfray

Ontario Game and Fishery Laws 1916

A paperback booklet of the Ontario Game and Fishery Laws 1916. The booklet is 91 pages in length and includes an index. See the full text in the Brock University Special Collections and Archives.

By-Laws No. 1 through 11

The by-laws are signed by George Barnes and include the first two which state the name of the company is the Ontario Grape Growing and Wine Manufacturing Company and the second by-law states that the place of business is at Barnesdale, St. Catharines, Ontario.