Pattern Formation in Traffic Microscopic Model

Apeltauer, Tomáš; Holcner, Petr; Macur, Jiri

doi:10.1007/978-3-540-77074-9_24

Cited by 3 publications

(2 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We assume that the road capacity (or traffic volume) q can be expressed as a time period in proportion to the sum of the length of vehicles and the distance between those vehicles. Neglecting the length of the vehicle, the hourly capacity (hourly traffic volume) can be expressed as [6] q h 3600 =…”

Section: Determination Of Traffic Patterns On Urban Roadsmentioning

confidence: 99%

Determination of Traffic Patterns on Urban Roads

Bartuška¹,

Jeřábek²,

Chenguang³

2017

Komunikácie

View full text Add to dashboard Cite

Section: Determination Of Traffic Patterns On Urban Roadsmentioning

confidence: 99%

Determination of Traffic Patterns on Urban Roads

Bartuška¹,

Jeřábek²,

Chenguang³

2017

Komunikácie

View full text Add to dashboard Cite

“…Nature is imprinted with patterns that are breathtakingly diverse in composition, self-engineered functionality, dimensionality, dynamism, and scale. − Several mechanisms have been proposed to explain the spontaneous emergence of patterns and symmetry breaking in homogeneous systems, which predominantly take place under nonlinear conditions. , Modulation instability (MI) is an exceptionally wide-reaching mechanism that describes the spontaneous emergence of patterns from the galactic to atomic length scales . In this stochastically driven process, noisenegligible perturbations in the otherwise homogeneous systembecomes greatly amplified under nonlinear conditions.…”

mentioning

confidence: 99%

Self-Organized Lattices of Nonlinear Optochemical Waves in Photopolymerizable Fluids: The Spontaneous Emergence of 3-D Order in a Weakly Correlated System

Ponte

Hudson

Saravanamuttu

2018

J. Phys. Chem. Lett.

View full text Add to dashboard Cite

Many of the extraordinary three-dimensional architectures that pattern our physical world emerge from complex nonlinear systems or dynamic populations whose individual constituents are only weakly correlated to each other. Shoals of fish, murmuration behaviors in birds, congestion patterns in traffic, and even networks of social conventions are examples of spontaneous pattern formation, which cannot be predicted from the properties of individual elements alone. Pattern formation at a different scale has been observed or predicted in weakly correlated systems including superconductors, atomic gases near Bose Einstein condensation, and incoherent optical fields. Understanding pattern formation in nonlinear weakly correlated systems, which are often unified through mathematical expression, could pave intelligent self-organizing pathways to functional materials, architectures, and computing technologies. However, it is experimentally difficult to directly visualize the nonlinear dynamics of pattern formation in most populations-especially in three dimensions. Here, we describe the collective behavior of large populations of nonlinear optochemical waves, which are poorly correlated in both space and time. The optochemical waves-microscopic filaments of white light entrapped within polymer channels-originate from the modulation instability of incandescent light traveling in photopolymerizable fluids. By tracing the three-dimensional distribution of optical intensity in the nascent polymerizing system, we find that populations of randomly distributed, optochemical waves synergistically and collectively shift in space to form highly ordered lattices of specific symmetries. These, to our knowledge, are the first three-dimensionally periodic structures to emerge from a system of weakly correlated waves. Their spontaneous formation in an incoherent and effectively chaotic field is counterintuitive, but the apparent contradiction of known behaviors of light including the laws of optical interference can be explained through the soliton-like interactions of optochemical waves with nearest neighbors. Critically, this work casts fundamentally new insight into the collective behaviors of poorly correlated nonlinear waves in higher dimensions and provides a rare, accessible platform for further experimental studies of these previously unexplored behaviors. Furthermore, it defines a self-organization paradigm that, unlike conventional counterparts, could generate polymer microstructures with symmetries spanning all the Bravais lattices.

show abstract