LANDSCAPE METRICS FROM THE POINT OF VIEW OF MATHEMATICAL LANDSCAPE MORPHOLOGY

This paper discusses potential of obtaining answers to key issues related to the use of landscape metrics by applying approaches of mathematical landscape morphology. Mathematical landscape morphology that has emerged in Russia’s geography in recent years serves as the basis of the new scientific direction in landscape science. Mathematical landscape morphology deals with quantitative regularities of the development of landscape patterns and methods of mathematical analysis. The results of the research conducted have demonstrated that landscape metrics are subjected to stochastic laws specific to genetic types of territories; furthermore, these laws may be derived through mathematical analysis. It has been also shown that the informational value of different landscape metrics differs and can be predicted. Finally, some landscape metrics, based on the values derived from single observations, nevertheless allow one to provide assessment of dynamic parameters of existing processes; thus, the volume of repeated monitoring observations could be reduced. Other metrics do not posses this characteristic. All results have been obtained by applying mathematical landscape modeling

RISK ASSESSMENT BASED ON MATHEMATICAL MORPHOLOGY OF LANDSCAPE MODELS (CASE STUDY OF THERMOKARST PLAINS)

Culte parmi d’autres dans une République laïque, l’islam demeure pourtant parfois associé à une part d’extranéité. Cette association s’observe dans le contentieux de la nationalité qui conduit le juge à mettre en relation les pratiques religieuses musulmanes des candidats à l’acquisition de la nationalité française et le respect de valeurs républicaines. Or, le contentieux récent lié à la législation visant à lutter contre le terrorisme présente sur ce point des similitudes terminologiques avec le précédent que cet article propose de mettre en lumière.While, in a secular Republic, the Muslim faith should be a denomination among others, it is nevertheless sometimes associated with “foreignness”. This association is observed in the nationality caselaw which leads the courts to relate the Muslim religious practices of candidates to the acquisition of French nationality and respect for republican values. However, recent cases related to anti-terrorism legislation look similar in terminology to the precedent, a similarity that this article intends to highlight

RISK ASSESSMENT BASED ON MATHEMATICAL MORPHOLOGY OF LANDSCAPE MODELS (CASE STUDY OF THERMOKARST PLAINS)

The paper presents a new approach for risk assessment of impact of thermokarst processes on engineering structures; it is based on the methods of mathematical morphology of landscape. The paper presents the results of the investigation of irregular (non-circular shape) thermokarst lakes. Remote sensing images of reference plots with thermokarst lakes were digitized; then, theoretical assumptions were applied and the simulation results were compared with empirical data to prove convergence. The analysis of the obtained results showed general agreement of empirical and theoretical data

Stochastic Models Of Dynamic Balance State For The Morphological Patterns Of Cryolithozone Landscapes

The paper deals with mathematical modeling of a morphological pattern for a broad spectrum of cryolithozone landscapes in a state of a dynamic balance. The state of the dynamic balance means that all the elements of this morphological pattern are in continuous changing while its general parameters as a whole are stable. Two contradirectional processes at the same territory is a precondition for a state of dynamic balance.We developed a morphological pattern model for lacustrine thermokarst plains with fluvial erosion on the base of the mathematical morphology of landscape using the random process theory. The contra-directional processes here include thermokarst lakes appearing and increasing in size from one side and drainage of the lakes by fluvial erosion, from the other. Thus, the regularities of the structure and dynamics of each landscape morphological pattern are theoretically substantiated. The results of the mathematical modeling were empirically verified at some key sites

Molecular Thermodynamics for Swelling of a Mesoscopic Ionomer Gel in 1:1 Salt Solutions

For a microphase-separated diblock copolymer ionic gel swollen in salt solution, a molecular-thermodynamic model is based on the self-consistent field theory in the limit of strongly segregated copolymer subchains. The geometry of microdomains is described using the Milner generic wedge construction neglecting the packing frustration. Thermodynamic functions are expressed analytically for gels of lamellar, bicontinuous, cylindrical and spherical morphologies. Molecules are characterized by chain composition, length, rigidity, degree of ionization, and by effective polymer-polymer and polymer-solvent interaction parameters. The model predicts equilibrium solvent uptakes and the equilibrium microdomain spacing for gels swollen in salt solutions. Results are given for details of the gel structure: distribution of mobile ions and polymer segments, and the electric potential across microdomains. Apart from effects obtained by coupling classical Flory-Rehner theory with Donnan equilibria, viz., increased swelling with polyelectrolyte charge and shrinking of gel upon addition of salt, the model predicts the effects of microphase morphology on swelling

Local Structure of Nonuniform Fluid Mixtures Containing Associating and Chainlike Molecules from a Multilayer Quasichemical Model

In this work, we develop a theory for predicting details of the local structure in nonuniform multicomponent fluids that may contain chainlike and associating components. This theory is an extensionto the fluid interfaces and mesoscopic structures of different geometryof the multilayer quasichemical model originally proposed by Smirnova to describe liquid solution in the vicinity of a planar solid wall. The basis of the theory is the “cut-and-bond” approach, much in spirit of SAFT, where an infinite attraction between the separated monomeric units of a chainlike molecule mimics the chemical bonds of the chain. We describe the equilibrium structure of the mixture, including the spatial distribution of the monomeric units and the local orientation of the chemical bonds in chainlike molecules, and discuss the contribution of chemical bonds to the local chemical potential in a nonuniform fluid. To test the new theory, we apply it to mixtures containing combinations of model components: a strongly associating solvent, an inert substance of varying chain length, and a chainlike amphiphile. To compare predictions from the multilayer model with the results of continuous description of nonuniform fluids, we also address the square-gradient theory and derive an analytical expression for the influence parameter that takes into account pair correlations in the quasichemical approximation. The multilayer quasichemical model developed in this work predicts formation of aggregates in liquid solution and describes the local structure of the interfaces between the coexisting liquid phases in the mixture. Our theoretical predictions agree on a qualitative level with the accumulated knowledge about the structure of different types of systems studied in this work

Modeling of the Effects of Ion Specificity on the Onset and Growth of Ionic Micelles in a Solution of Simple Salts

A new version of the molecular thermodynamic model has been developed that takes into account the effect of ion specificity on the free energy of aggregation. The specificity of salt is reflected by differences in the bare ionic sizes and polarizabilities leading to the difference in the dispersion interaction of ions with the aggregate. The model also contains parameters that characterize the compactness of ionic pairs formed between a mobile ion and surfactant’s headgroup. The values of these parameters show that more chaotropic heads form tighter pairs with chaotropic ions whereas more cosmotropic heads form more compact pairs with cosmotropic ions. The formation of compact pairs in the micelle corona diminishes the preferable curvature of the aggregates and promotes their growth. The model has been applied to aqueous solutions of cationic (alkyltrimethylammonium, alkyldimethylammonium, and alkylpyridinium) and anionic (alkylsulfate and alkylcarboxylate) surfactants in the presence of simple 1:1 salts. With a single set of parameter values, the model reproduces the critical micelle concentration–salinity curves and the sphere-to-rod transitions or the absence of thereof and describes the aggregate growth for different simple salts, in good agreement with experiment

Research into Cryolithozone Spatial Pattern Changes Based on the Mathematical Morphology of Landscapes

Lacustrine thermokarst is receiving great interest as a landscape-forming process. Despite this, research dealing with the quantitative analysis of the changes in the morphological patterns of thermokarst plains under ongoing climate change is lacking. This study aims to analyze changes in the morphological patterns of cryolithozone landscapes based on models provided by the mathematical morphology of landscapes. Our research involves eight key sites within lacustrine thermokarst plains and nine key sites within thermokarst plains with fluvial erosion. These sites differ in geomorphological, geocryological, and physiographical terms, and are situated in different regions such as Yamal, Taimyr, Kolyma lowland, river Lena delta, Baffin’s Land, and Alaska. Archival Corona images (date 1) and high-resolution satellite imagery from June to August 2008–2014 (date 2) were used to obtain the model’s morphometric data. According to quantitative analysis of the models, the morphological pattern of the lacustrine thermokarst plains did not undergo significant changes during the observation period, while 20% of the key sites within the thermokarst plains with fluvial erosion underwent essential changes in lake area distributions. This difference may come from the higher reactivity of the fluvial erosion process on climate change than that of the thermokarst