Reactions, Diffusion and Volume Exclusion in a Heterogeneous System of Interacting Particles

Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and reactions between heterogenous particles is less well known. In this paper we develop a novel framework for modeling reaction-diffusion processes which directly incorporates volume exclusion. From an off-lattice microscopic individual based model we use the Fokker--Planck equation and the method of matched asymptotic expansions to derive a low-dimensional macroscopic system of nonlinear partial differential equations describing the evolution of the particles. A biologically motivated, hybrid model of chemotaxis with volume exclusion is explored, where reactions occur at rates dependent upon the chemotactic environment. Further, we show that for reactions due to contact interactions the appropriate reaction term in the macroscopic model is of lower order in the asymptotic expansion than the nonlinear diffusion term. However, we find that the next reaction term in the expansion is needed to ensure good agreement with simulations of the microscopic model. Our macroscopic model allows for more direct parameterization to experimental data than the models available to date.Comment: 13 pages, 4 figure

Fragmented molecular complexes: The role of the magnetic field in feeding internal supersonic motions

A hierarchical structure for molecular complexes in their cold phase i.e., preceeding the formation of massive stars, was derived from extensive large scale CO(13)(J=1=0) observations: the mass is found to be distributed into virialized clouds which fill only a very low fraction approx. 01 of the volume of the complex and are supported against gravity by internal supersonic motions. An efficient mechanism was found to transfer kinetic energy from the orbital motions of the clouds to their internal random motions. The large perturbations of the magnetic field induced at the cloud boundaries by their interactions with their neighbors generate systems of hydromagnetic waves trapped inside the clouds. The magnetic field lines being closely coupled to the gas at the densities which prevail in the bulk of the clouds volume, internal velocity dispersion is thus generated. Some conclusions derived from this data are given

Grammatical gender and linguistic complexity II: World-wide comparative studies

The many facets of grammatical gender remain one of the most fruitful areas of linguistic research, and pose fascinating questions about the origins and development of complexity in language. The present work is a two-volume collection of 13 chapters on the topic of grammatical gender seen through the prism of linguistic complexity. The contributions discuss what counts as complex and/or simple in grammatical gender systems, whether the distribution of gender systems across the world’s languages relates to the language ecology and social history of speech communities. Contributors demonstrate how the complexity of gender systems can be studied synchronically, both in individual languages and over large cross-linguistic samples, and diachronically, by exploring how gender systems change over time. Volume two consists of three chapters providing diachronic and typological case studies, followed by a final chapter discussing old and new theoretical and empirical challenges in the study of the dynamics of gender complexity. This volume is preceded by volume one, which, in addition to three chapters on the theoretical foundations of gender complexity, contains six chapters on grammatical gender and complexity in individual languages and language families of Africa, New Guinea, and South Asia

Grammatical gender and linguistic complexity II: World-wide comparative studies

The many facets of grammatical gender remain one of the most fruitful areas of linguistic research, and pose fascinating questions about the origins and development of complexity in language. The present work is a two-volume collection of 13 chapters on the topic of grammatical gender seen through the prism of linguistic complexity. The contributions discuss what counts as complex and/or simple in grammatical gender systems, whether the distribution of gender systems across the world’s languages relates to the language ecology and social history of speech communities. Contributors demonstrate how the complexity of gender systems can be studied synchronically, both in individual languages and over large cross-linguistic samples, and diachronically, by exploring how gender systems change over time. Volume two consists of three chapters providing diachronic and typological case studies, followed by a final chapter discussing old and new theoretical and empirical challenges in the study of the dynamics of gender complexity. This volume is preceded by volume one, which, in addition to three chapters on the theoretical foundations of gender complexity, contains six chapters on grammatical gender and complexity in individual languages and language families of Africa, New Guinea, and South Asia

Grammatical gender and linguistic complexity II: World-wide comparative studies

The many facets of grammatical gender remain one of the most fruitful areas of linguistic research, and pose fascinating questions about the origins and development of complexity in language. The present work is a two-volume collection of 13 chapters on the topic of grammatical gender seen through the prism of linguistic complexity. The contributions discuss what counts as complex and/or simple in grammatical gender systems, whether the distribution of gender systems across the world’s languages relates to the language ecology and social history of speech communities. Contributors demonstrate how the complexity of gender systems can be studied synchronically, both in individual languages and over large cross-linguistic samples, and diachronically, by exploring how gender systems change over time. Volume two consists of three chapters providing diachronic and typological case studies, followed by a final chapter discussing old and new theoretical and empirical challenges in the study of the dynamics of gender complexity. This volume is preceded by volume one, which, in addition to three chapters on the theoretical foundations of gender complexity, contains six chapters on grammatical gender and complexity in individual languages and language families of Africa, New Guinea, and South Asia

Grammatical gender and linguistic complexity I: General issues and specific studies

The many facets of grammatical gender remain one of the most fruitful areas of linguistic research, and pose fascinating questions about the origins and development of complexity in language. The present work is a two-volume collection of 13 chapters on the topic of grammatical gender seen through the prism of linguistic complexity. The contributions discuss what counts as complex and/or simple in grammatical gender systems, whether the distribution of gender systems across the world’s languages relates to the language ecology and social history of speech communities. Contributors demonstrate how the complexity of gender systems can be studied synchronically, both in individual languages and over large cross-linguistic samples, and diachronically, by exploring how gender systems change over time. In addition to three chapters on the theoretical foundations of gender complexity, volume one contains six chapters on grammatical gender and complexity in individual languages and language families of Africa, New Guinea, and South Asia. This volume is complemented by volume two, which consists of three chapters providing diachronic and typological case studies, followed by a final chapter discussing old and new theoretical and empirical challenges in the study of the dynamics of gender complexity