Entropy of Open Lattice Systems

We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different densities. In the hydrodynamic scaling limit, L to infinity, the leading order (O(L)) behavior of this entropy has been shown by Bahadoran to be that of a product measure corresponding to strict local equilibrium; we compute the first correction, which is O(1). The computation uses a formal expansion of the entropy in terms of truncated correlation functions; for this system the k-th such correlation is shown to be O(L^{-k+1}). This entropy correction depends only on the scaled truncated pair correlation, which describes the covariance of the density field. It coincides, in the large L limit, with the corresponding correction obtained from a Gaussian measure with the same covariance.Comment: Latex, 28 pages, 4 figures as eps file

Shift Equivalence of Measures and the Intrinsic Structure of Shocks in the Asymmetric Simple Exclusion Process

We investigate properties of non-translation-invariant measures, describing particle systems on \bbz, which are asymptotic to different translation invariant measures on the left and on the right. Often the structure of the transition region can only be observed from a point of view which is random---in particular, configuration dependent. Two such measures will be called shift equivalent if they differ only by the choice of such a viewpoint. We introduce certain quantities, called translation sums, which, under some auxiliary conditions, characterize the equivalence classes. Our prime example is the asymmetric simple exclusion process, for which the measures in question describe the microscopic structure of shocks. In this case we compute explicitly the translation sums and find that shocks generated in different ways---in particular, via initial conditions in an infinite system or by boundary conditions in a finite system---are described by shift equivalent measures. We show also that when the shock in the infinite system is observed from the location of a second class particle, treating this particle either as a first class particle or as an empty site leads to shift equivalent shock measures.Comment: Plain TeX, 2 figures; [email protected], [email protected], [email protected], [email protected]

Experiments with potatoes in 1889-1890

It is more difficult to improve the potato, (Solanum tuberosum) by the production of new varieties from seeds, than any other common field or garden vegetable. Although hundreds of promising kinds are produced every year, yet none of the new varieties is better than the old Mercer, Pink Eye, Snow Flake, Early Goodrich or Jersey Peach-blow. No other experiments have been tried oftener, than the planting of big potatoes against little ones or pieces with several eyes or single eyes, yet nothing has been gained by such experiments. Sometimes the little potatoes or the single eyes come out ahead; but generally, about the time that the results appear to be satisfactory, somebody else gets very different results. I have conducted such experiments and many others, without being able to discover why potatoes are inclined to degenerate, or why the single eye pieces come out ahead one year and fall behind the next. In 1888, we planted about 80 varieties of potatoes on our experiment grounds. All of the seed potatoes had been carefully assorted, and they were cut into two and three-eyed pieces as nearly alike in size as possible. The planting of all of the varieties was done on the 21st day of May in the same manner, and they received the same cultivation during the following summer. About the time the early varieties were flowering, I observed that all of the stalks or vines of certain kinds were of the same size and equally vigorous, and that there were great differences between the vines of other varieties. In some of the rows I found the vines of one-third of the hills very vigorous; another third was much less thrifty, and the remaining third were small and appeared to be unhealthy. When we dug the potatoes in the fall, I found as great differences between the products of the hills of the different varieties, as I had found between the vines while they were growing. I was convinced that the discovery of the causes of such differences would show that all of the faults were in the pieces of seed potatoes, and I determined to give the matter special attention during the following summer. About the 1st of May, ’89, I examined our seed potatoes which had been stored in bushel boxes in an out-door cellar, and found that the early varieties had produced sprouts from their seed ends from two to three inches long; but all of the eyes or buds on their stem ends were dormant. I had observed the early sprouting of the seed ends of potatoes often before, and I knew that the terminal buds of trees always started first, and that their stems grew upwards and their roots downwards; but I did not inquire for causes, as I supposed it was their nature to do so. Before leaving the cellar, the question occurred to me: If I should plant the vigorous buds from the seed ends of the potatoes, would they produce a better or a worse crop, than weak and dormant buds from their stem ends? I knew that both ends of the potatoes were well supplied with starch; but I thought that the difference between the starting of the eyes might be caused by a scarcity of albuminoids in their stem ends

Sugar experiments

The United States imports $120,000,000 worth of sugar annually from foreign countries. As we have a great diversity of climate and 110 other country has better soils, it is remarkable that greater efforts have not been made to produce it at home and prevent our money from going abroad. Sugar cane is the only plant from which sugar was made in considerable quantities in this country prior to last year, and it can be grown profitably only within limited areas of Louisiana and Texas. But the results of the experiments which were made with sorghum last year and this year, indicate that skill and suitable machinery is all that is needed to make sugar from it profitably in Kansas and other western states. Since the introduction of Amber cane, only ordinary care has been necessary to produce good syrup cheaply in Iowa, which has generally shown a strong tendency to granulate. This variety of sorghum has proved to be one of our most reliable crops and rich in sucrose; but it is generally understood that sugar can not be extracted from it profitably, except by the use very costly machinery in large factories. I f such belief is well founded, then sugar can not be made in large quantities in Iowa, because the time (twenty to thirty days) is too short between the ripening of the canes and frost, to warrant the expenditure of very large sums of money in sugar factories. But such work can be done as well in small factories as large ones, and that others may judge whether I am right or not, I will explain the principle troubles which are always encountered in making sugar from sorghum and sugar cane. Sucrose is cane sugar, which crystallizes readily when surrounded by favorable conditions, and glucose is grape sugar, which can not be crystallized by the ordinary processes for making sugar

Our rusted and blighted wheat, oats and barley in 1890

In 1888 we sowed many kinds of oats, wheat, and barley, but all of them were so much injured by rust, that they were scarcely worth harvesting. In 1889 we sowed them again, and a considerable number of them proved productive, and showed no signs of disease; while others suffered severely from rust, although the growing season was much more favorable for such crops than the preceding one. In 1890 we discarded certain varieties which had proved unreliable and procured others that were promising. On the 26th day of last March, the following kinds of oats were sown broadcast on ground which had produced eighty bushels of shelled corn per acre in 1889, viz: Hargett’s White Seizure, Carter’s Prize Cluster, Station Prize Cluster, Pringle’s Progress, Prince Edward’s Island, American Beauty, Everett’s Scottish Chief, Black Russian, White Russian, Black Prolific, Black Tartarian, Salzer’s White Wonder, White Australian, American Banner, Wide Awake, Race Horse, Badger Queen, White Victoria, Henderson’s Clydesdale, White Bonanza, Centennial, Currie’s Prize Cluster, Welcome, Wilson’s Prolific side oats, Baltic Oats, Giant Yellow French, Lackawana, Golden Giant side oats, Everett side oats, and Improved American Oats. The ground was divided into six long plats by lines running from the east end of the field towards the west, and the plats were numbered from the north to the south side as follow s : 1, 2, 3, 4, 5, and 6. All of the plats were plowed six inches deep, except plat 3 which was not plowed at all. The plowing of plats, 1, 5 and 6 was done in the fall o f 1889, and plats 2 and 4 were plowed on the 25th day of last March. No crops had ever been grown on plat