1,543 Result(s)
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Chapter
Da**g **a
Biological and Medical Physics, Biophysics
Complex Systems
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Chapter
6 Patterns of Active Matter
Active systems do not require external energy input in an explicit form, as sketched in Fig. 1.1, but are capable of independent motion. Of course, a hidden energy input is always present, in the form of chemi...
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1 Genesis of Patterns
An open system is sustained in a nonequilibrium state by external fluxes. Such a system, generally, can be assigned no energy functional; its dynamics is more interesting, since it is not restricted by a priori r...
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3 Structures with Sharp Interfaces
A reaction-diffusion model with separated scales suitable for generation of a variety of patterns is a two-component system including a short-range activator u and a long-range inhibitor v, written in a general f...
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5 Irregular Wave Patterns
The complex Ginzburg–Landau (CGL) equation (1.1.6) has been derived in Sect. 1.3.3 as the amplitude equation (1.3.28) at the Hopf bifurcation that describes the evolution of the oscillation amplitude on a slow...
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Chapter
Introduction
The human eye is bored by monotonous landscapes. We are depressed by gray skies, unending plains under the wing of an airliner, featureless urban sprawl, geometric canvasses in empty museum halls. Having evolv...
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2 Fronts between Uniform States
The function f(u) may depend on a number of parameters modifying its shape. In particular, the cubic equation (1.2.18) obtained at the cusp singularity with added diffusional term can be seen as the simplest mode...
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4 Irregular Stationary Patterns
The real Ginzburg–Landau equation (RGL) (1.1.7) is the simplest pattern-forming system derived in Sect. 1.3.3 as the amplitude equation describing long-scale modulations near a cusp bifurcation point. The wave...
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Calcium Signaling Along Actin Filaments in Stereocilia Controls Hair-Bundle Motility
Actin is the most abundant protein in eukaryotic cells. It is highly evolutionary conserved and takes part in more protein–protein interactions than any other known protein. These characteristics, along with i...
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Random Simplicial Complexes: Models and Phenomena
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for ...
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The Insights into Richness of Nonlinear Schrödinger Equation
The nonlinear Schrödinger equation (NLSE) plays an important role in modelling a large number of phenomena of various branches of science to significant accuracy. In this chapter methodology has been discussed...
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Flow-Based Community Detection in Hypergraphs
To connect structure, dynamics and function in systems with multibody interactions, network scientists model random walks on hypergraphs and identify communities that confine the walks for a long time. The two...
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Nonlinear Dynamics of DNA Chain with Long-Range Interactions
The present chapter is devoted to the investigation of the nonlinear dynamics of DNA molecules in the helicoidal Peyrard-Bishop DNA model with long-range interactions. The power law long-range interactions wit...
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Non-pairwise Interaction in Oscillatory Ensembles: from Theory to Data Analysis
In this chapter, we briefly review several cases when non-pairwise interaction naturally appears in oscillatory networks. First, we analyze globally coupled ensembles of phase oscillators. We demonstrate that ...
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Geometry, Topology and Simplicial Synchronization
Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in th...
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Conformational B-A-Transition in the DNA Molecule Model
Nucleic acids play a major role in the storage and implementation of genetic information. There are two types of nucleic acids: deoxyribonucleic acids (DNA), which provide information storage, and ribonucleic aci...
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Explosive Synchronization and Multistability in Large Systems of Kuramoto Oscillators with Higher-Order Interactions
Since its original formulation, the Kuramoto model and its many variants have served as critical tools for uncovering and understanding the emergence of nonlinear collective behavior. However, recent evidence ...
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Social Contagion on Higher-Order Structures
In this Chapter, we discuss the effects of higher-order structures on SIS-like processes of social contagion. After a brief motivational introduction where we illustrate the standard SIS process on networks an...
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Vibron Self-trap** in Quasi-One-Dimensional Biomolecules: Non-adiabatic Polaron Approach
The high efficiency of the biophysical processes occurring inside living cells is one of the elementary preconditions of their functioning. Unfortunately, this is quite difficult to understand from the point o...
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Collective Games on Hypergraphs
Human activities often require simultaneous decision-making of individuals in groups. These processes cannot be coherently addressed by means of networks, as networks only allow for pairwise interactions. Here...
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Higher-Order Description of Brain Function
Higher-order interactions have long figured both at the microscopic and macroscopic level in neuronal and whole-brain descriptions, with the aim to capture structural, functional, and ultimately cognitive aspe...
