Behavior of the reaction front between initially segregated species in a two-stage reaction

The large-time asymptotic behavior of a two-stage reaction (A+B→R, B+R→S) with initially segregated reactants is described. The concentration of the reactants is found to be significantly less than the initial concentrations in a depletion zone of width proportional to t[sup. 1/2], where t is time; the reaction takes place in a thinner zone of width proportional to t[sup. 1/6]. Similarity solutions for the chemical concentration profiles in the reaction zone are calculated, and are compared with numerical simulations of the full partial differential reaction-diffusion equations. The large-time asymptotic scalings reported here are the same as in the absence of the secondary reaction, but we find that the location of the reaction zone is significantly shifted due to the secondary reaction. The reaction zone may behave in an exotic fashion at large time, moving first one way, then reversing its direction.Stephen M. Cox and Matthew D. Fin

Surnames in Texas: a population study through isonymy.

To study the isonymy structure of Texas, we analyzed the surname distributions of 3.6 million telephone users registered for the year 1996 in 232 towns distributed in the 7 regions of the state. The number of different surnames was 235,740. Matrices of isonymy distances between towns and between geographic regions were constructed and tested for correlation with geographic distance. We found that isonymy distances between the seven regions showed borderline or no correlation with geographic distance, with r = 0.089 +/- 0.232, r = 0.492 +/- 0.232, and r = 0.337 +/- 0.232 for Lasker's, Euclidean, and Nei's distances, respectively. Isonymy distances between towns were significantly correlated with geographic distance, with r = 0.249 +/- 0.006 for Lasker's distance, r = 0.338 +/- 0.006 for the Euclidean distance, and r = 0.418 +/- 0.006 for Nei's distance. Two dendrograms, one for the 7 regions and one for the 232 towns, were built from the matrices of Nei's distances. The dendrogram for regions indicates that a main surname differentiation exists between the East and West areas of Texas, with West Texas being predominantly Hispanic and East Texas being predominantly English-speaking. The dendrogram for the towns confirms in detail the differences identified by the matrix of distances between regions. Random inbreeding calculated from isonymy, F(ST), was highest in the west and in the south of the state. It was lowest in the area of Austin and Houston. Average Fisher's alpha for towns was 734, for regions it was 1,047, and for Texas as a whole it was 1,230. The geographic distribution of alpha in the state shows distinctly lower values in the traditionally Hispanic west and higher values in the east and on the Gulf of Mexico

ISONYMY AND ISOLATION BY DISTANCE IN ITALY

The isonymy structure of Italy was studied using the surname distribution of 5,043,580 private telephone users selected from a 1996 commercial CD-ROM that contains all 24 million users in the country. The users were distributed in 123 towns selected on a geographic basis. The 123 towns were either on the main communication roads of the country or at the ends of such roads. The shortest distance between nearest neighbor towns was 5.3 km (Carrara and Massa), and the largest distance was 1,136 km (Aosta and Castrignano del Capo). The number of different surnames found in the whole analysis was 215,623. Lasker's distance, the negative value of the logarithm of random isonymy between localities, was linearly and significantly correlated with the logarithm of geographic distance, with r = 0.63 +/- 0.008. A dendrogram was built from the matrix of isonymy distances, using UPGMA. It separates the Italian towns into 5 main clusters: 1 in the southern portion of the country, a second cluster toward the center, and 3 in the northern area of Italy. Within each cluster small subclusters with specific geographic distributions could be related to regional borders. Comparisons with the results of a previous analysis of Switzerland and Germany's structures are given. From the present analysis isolation by distance emerges clearly, although it is less strong than in Switzerland and stronger than in Germany. The random component of inbreeding estimated from isonymy indicates that the southern area of Italy is on average more inbred than the northern area. In fact, the heterogeneity is greater in the northern area, particularly in the plain of the Po River, than anywhere else in Ital

Surnames in Texas: A Population Study Through Isonymy

To study the isonymy structure of Texas, we analyzed the surname distributions of 3.6 million telephone users registered for the year 1996 in 232 towns distributed in the 7 regions of the state. The number of different surnames was 235,740. Matrices of isonymy distances between towns and between geographic regions were constructed and tested for correlation with geographic distance. We found that isonymy distances between the seven regions showed borderline or no correlation with geographic distance, with r = 0.089 ± 0.232, r = 0.492 ± 0.232, and r = 0.337 ± 0.232 for Lasker’s, Euclidean, and Nei’s distances, respectively. Isonymy distances between towns were significantly correlated with geographic distance, with r = 0.249 ± 0.006 for Lasker’s distance, r = 0.338 ± 0.006 for the Euclidean distance, and r = 0.418 ± 0.006 for Nei’s distance. Two dendrograms, one for the 7 regions and one for the 232 towns, were built from the matrices of Nei’s distances. The dendrogram for regions indicates that a main surname differentiation exists between the East and West areas of Texas, with West Texas being predominantly Hispanic and East Texas being predominantly English-speaking. The dendrogram for the towns confirms in detail the differences identified by the matrix of distances between regions. Random inbreeding calculated from isonymy, FST , was highest in the west and in the south of the state. It was lowest in the area of Austin and Houston. Average Fisher’s α for towns was 734, for regions it was 1,047, and for Texas as a whole it was 1,230. The geographic distribution of α in the state shows distinctly lower values in the traditionally Hispanic west and higher values in the east and on the Gulf of Mexico

Isonymy and Isolation by Distance in Italy

The isonymy structure of Italy was studied using the surname distribution of 5,043,580 private telephone users selected from a 1996 commercial CD-ROM that contains all 24 million users in the country. The users were distributed in 123 towns selected on a geographic basis. The 123 towns were either on the main communication roads of the country or at the ends of such roads. The shortest distance between nearest neighbor towns was 5.3 km (Carrara and Massa), and the largest distance was 1,136 km (Aosta and Castrignano del Capo). The number of different surnames found in the whole analysis was 215,623. Lasker’s distance, the negative value of the logarithm of random isonymy between localities, was linearly and significantly correlated with the logarithm of geographic distance, with r = 0.63 ± 0.008. A dendrogram was built from the matrix of isonymy distances, using UPGMA. It separates the Italian towns into 5 main clusters: 1 in the southern portion of the country, a second cluster toward the center, and 3 in the northern area of Italy. Within each cluster small subclusters with specific geographic distributions could be related to regional borders. Comparisons with the results of a previous analysis of Switzerland and Germany’s structures are given. From the present analysis isolation by distance emerges clearly, although it is less strong than in Switzerland and stronger than in Germany. The random component of inbreeding estimated from isonymy indicates that the southern area of Italy is on average more inbred than the northern area. In fact, the heterogeneity is greater in the northern area, particularly in the plain of the Po River, than anywhere else in Italy

The names of Spain: A study of the isonymy structure of Spain

In order to estimate the isonymy structure of Spain, we studied surname distribution in 283 Spanish towns based on 3.625 million telephone users selected from 6.328 million users, downloaded from a commercial CD-ROM which contains all 13 million users in the country. Since in Spain the surname is made by the paternal and the maternal surname, it was possible to classify surnames according to parental origin. Two matrices of isonymy distances, one for paternal and one for maternal surnames, were constructed and tested for correlation with geographic distance. For the whole of Spain, Euclidean distance was significantly but weakly correlated with geographic distance both for paternal and maternal surnames, with r = 0.205 +/- 0.013 and r = 0.263 +/- 0.012, respectively. Two dendrograms of the 283 sampled towns were built from the two matrices of Euclidean distance. They are largely colinear. Four main clusters identified by the dendrograms are correlated with geography. Given the surname structure of Spain, we were able to calculate from isonymy and for each town 1). total or expressed inbreeding, 2). random or expected inbreeding, and 3). local inbreeding. Total inbreeding, F(IT), was highest in the North Atlantic regions and lowest along the Mediterranean Coast. The lowest levels were found in Andalusia, Catalunyia, Valencia, and Navarra. Random inbreeding, F(ST), had a similar geographical pattern. Local inbreeding, F(IS), was relatively uniform in the whole of Spain. In towns, random inbreeding dominates over local inbreeding. From the analysis, it emerges that the northwestern area of Spain is the most inbred

Isonymy and isolation by distance in the Netherlands

The isonymy structure of the Netherlands was studied using the surname distribution of 2.4 million private telephone users selected from a 1996 commercial CD-ROM containing the names of 6.3 million users in the country. The users were distributed in 226 towns selected on a geographic basis to form an approximately regular grid throughout the Netherlands. Names of telephone users in each town were downloaded from the CD-ROM, with private users being selected for inclusion in the analysis. The shortest linear distance between several nearest neighboring towns was less than 2 km (e.g., Kampen and Ijsselmuiden, Krommen and Zaandijk, Hendrikdo and Papendrecht) and the longest distance was 326 km (Delfzijl and Oostburg ZL). The number of different surnames revealed by the analysis was 126,485. Lasker's distance, the negative value of the logarithm of isonymy between localities, was found to be significantly correlated with linear geographic distance, with r = 0.47 +/- 0.006. A dendrogram built using the matrix of isonymy distances, using the nearest neighbor-joining method, separates the Dutch towns into several clusters, most of them correlated with traditional Dutch regions. Comparisons with the results of previous analyses of the structure of other European countries are given. From the present analysis, isolation by distance emerges clearly, and it is relevant, although much weaker than in Switzerland, Austria, Italy, and Germany. The random component of inbreeding estimated from isonymy indicates a considerable degree of homogeneity in the Netherland

Isonymy and Isolation by Distance in the Netherlands

The isonymy structure of the Netherlands was studied using the surname distribution of 2.4 million private telephone users selected from a 1996 commercial cd-rom containing the names of 6.3 million users in the country. The users were distributed in 226 towns selected on a geographic basis to form an approximately regular grid throughout the Netherlands. Names of telephone users in each town were downloaded from the cd-rom, with private users being selected for inclusion in the analysis. The shortest linear distance between several nearest neighboring towns was less than 2 km (e.g., Kampen and Ijsselmuiden, Krommen and Zaandijk, Hendrikdo and Papendrecht) and the longest distance was 326 km (Delfzijl and Oostburg ZL). The number of different surnames revealed by the analysis was 126,485. Lasker’s distance, the negative value of the logarithm of isonymy between localities, was found to be significantly correlated with linear geographic distance, with r = 0.47 ± 0.006. A dendrogram built using the matrix of isonymy distances, using the nearest neighbor-joining method, separates the Dutch towns into several clusters, most of them correlated with traditional Dutch regions. Comparisons with the results of previous analyses of the structure of other European countries are given. From the present analysis, isolation by distance emerges clearly, and it is relevant, although much weaker than in Switzerland, Austria, Italy, and Germany. The random component of inbreeding estimated from isonymy indicates a considerable degree of homogeneity in the Netherlands