2,812 research outputs found
Traveling and pinned fronts in bistable reaction-diffusion systems on network
Traveling fronts and stationary localized patterns in bistable
reaction-diffusion systems have been broadly studied for classical continuous
media and regular lattices. Analogs of such non-equilibrium patterns are also
possible in networks. Here, we consider traveling and stationary patterns in
bistable one-component systems on random Erd\"os-R\'enyi, scale-free and
hierarchical tree networks. As revealed through numerical simulations,
traveling fronts exist in network-organized systems. They represent waves of
transition from one stable state into another, spreading over the entire
network. The fronts can furthermore be pinned, thus forming stationary
structures. While pinning of fronts has previously been considered for chains
of diffusively coupled bistable elements, the network architecture brings about
significant differences. An important role is played by the degree (the number
of connections) of a node. For regular trees with a fixed branching factor, the
pinning conditions are analytically determined. For large Erd\"os-R\'enyi and
scale-free networks, the mean-field theory for stationary patterns is
constructed
Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation
Cellular differentiation in a developping organism is studied via a discrete
bistable reaction-diffusion model. A system of undifferentiated cells is
allowed to receive an inductive signal emenating from its environment.
Depending on the form of the nonlinear reaction kinetics, this signal can
trigger a series of bifurcations in the system. Differentiation starts at the
surface where the signal is received, and cells change type up to a given
distance, or under other conditions, the differentiation process propagates
through the whole domain. When the signal diminishes hysteresis is observed
Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions
Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities—both at the microstructural scale in materials and at the macroscopic, structural level—lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials
Lattice Gas Automata for Reactive Systems
Reactive lattice gas automata provide a microscopic approachto the dynamics
of spatially-distributed reacting systems. After introducing the subject within
the wider framework of lattice gas automata (LGA) as a microscopic approach to
the phenomenology of macroscopic systems, we describe the reactive LGA in terms
of a simple physical picture to show how an automaton can be constructed to
capture the essentials of a reactive molecular dynamics scheme. The statistical
mechanical theory of the automaton is then developed for diffusive transport
and for reactive processes, and a general algorithm is presented for reactive
LGA. The method is illustrated by considering applications to bistable and
excitable media, oscillatory behavior in reactive systems, chemical chaos and
pattern formation triggered by Turing bifurcations. The reactive lattice gas
scheme is contrasted with related cellular automaton methods and the paper
concludes with a discussion of future perspectives.Comment: to appear in PHYSICS REPORTS, 81 revtex pages; uuencoded gziped
postscript file; figures available from [email protected] or
[email protected]
Phenotypic Variation and Bistable Switching in Bacteria
Microbial research generally focuses on clonal populations. However, bacterial cells with identical genotypes frequently display different phenotypes under identical conditions. This microbial cell individuality is receiving increasing attention in the literature because of its impact on cellular differentiation, survival under selective conditions, and the interaction of pathogens with their hosts. It is becoming clear that stochasticity in gene expression in conjunction with the architecture of the gene network that underlies the cellular processes can generate phenotypic variation. An important regulatory mechanism is the so-called positive feedback, in which a system reinforces its own response, for instance by stimulating the production of an activator. Bistability is an interesting and relevant phenomenon, in which two distinct subpopulations of cells showing discrete levels of gene expression coexist in a single culture. In this chapter, we address techniques and approaches used to establish phenotypic variation, and relate three well-characterized examples of bistability to the molecular mechanisms that govern these processes, with a focus on positive feedback.
Dissipative solitons in pattern-forming nonlinear optical systems : cavity solitons and feedback solitons
Many dissipative optical systems support patterns. Dissipative solitons are generally found where a pattern coexists with a stable unpatterned state. We consider such phenomena in driven optical cavities containing a nonlinear medium (cavity solitons) and rather similar phenomena (feedback solitons) where a driven nonlinear optical medium is in front of a single feedback mirror. The history, theory, experimental status, and potential application of such solitons is reviewed
Feedback-induced stationary localized patterns in networks of diffusively coupled bistable elements
Effects of feedbacks on self-organization phenomena in networks of diffusively coupled bistable elements are investigated. For regular trees, an approximate analytical theory for localized stationary patterns under application of global feedbacks is constructed. Using it, properties of such patterns in different parts of the parameter space are discussed. Numerical investigations are performed for large random Erdös-Rényi and scale-free networks. In both kinds of systems, localized stationary activation patterns have been observed. The active nodes in such a pattern form a subnetwork, whose size decreases as the feedback intensity is increased. For strong feedbacks, active subnetworks are organized as trees. Additionally, local feedbacks affecting only the nodes with high degrees (i.e., hubs) or the periphery nodes are considered
- …