Cover Time on a Square Lattice by Two Colored Random Walkers

The influence of information on the pedestrian in crowd dispersion process is investigated under the open boundary condition on the square lattice by the use of the lattice gas model of biased random walkers without the back step. It is found that the jamming phenomenon occurs when the total entrance density is small in spite of influence of information. The mean velocity 〈v〉 ped of the walkers moving remains a constant via a small fluctuation for the small total entrance density, but for the large total entrance density, the 〈v〉 ped increases from 0 to 1. The mean velocity 〈v〉 inf of information spreading increases from 0 to 1, and then decreases to 0. The critical density decreases with increasing the size W of the system. When the size of the system is small, the platform appears because of asymmetry in propagation of information.

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A random-walk-based epidemiological model

Scientific Reports ◽

10.1038/s41598-021-98211-5 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Andrew Chu ◽

Greg Huber ◽

Aaron McGeever ◽

Boris Veytsman ◽

David Yllanes

Keyword(s):

Random Walk ◽

Functional Dependence ◽

Universality Class ◽

Simple Random Walk ◽

Basic Reproductive Number ◽

Square Lattice ◽

Reproductive Number ◽

Random Walkers ◽

Spatial Fluctuations ◽

Spatio Temporal

AbstractRandom walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates non-trivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The functional dependence of the basic reproductive number $$R_{0}$$ R 0 on the model’s defining parameters reveals the role of spatial fluctuations and leads to a novel expression for $$R_{0}$$ R 0 . Special attention is given to simulations of inter-regional transmission of the contagion. The scaling of the epidemic with respect to space and time scales is studied in detail in the critical region, which is shown to be compatible with the directed-percolation universality class.

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A random-walk based epidemiological model

10.1101/2020.11.04.20226308 ◽

2020 ◽

Author(s):

Andrew Chu ◽

Greg Huber ◽

Aaron McGeever ◽

Boris Veytsman ◽

David Yllanes

Keyword(s):

Random Walk ◽

Functional Dependence ◽

Simple Random Walk ◽

Basic Reproductive Number ◽

Square Lattice ◽

Reproductive Number ◽

Radius Of Gyration ◽

Epidemic Dynamics ◽

Random Walkers ◽

Spatio Temporal

ABSTRACTRandom walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates nontrivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The phase boundary separating those sets of parameters leading to outbreaks dying out and those leading to indefinite growth is mapped out in detail. The functional dependence of the basic reproductive number R0 on the model’s defining parameters reveals the role of spatial fluctuations and leads to a novel expression for R0. Special attention is given to simulations of inter-regional transmission of the contagion. The attack rate and the (growing) radius of gyration of the affected zones are used as measures of the severity of the outbreaks, in cases where R0 is not sufficiently prescriptive to chart the epidemic dynamics.

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Trapping of biological random walkers Part 2: Field results of single-trap, multiple-release experiments with codling moth,Cydia pomonella

10.1603/ice.2016.112869 ◽

2016 ◽

Author(s):

Christopher G. Adams

Keyword(s):

Cydia Pomonella ◽

Codling Moth ◽

Random Walkers

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Trapping of biological random walkers Part 3: Two-dimensional heat equation as the foundation for translating catch number into absolute pest density

10.1603/ice.2016.112820 ◽

2016 ◽

Author(s):

James R. Miller

Keyword(s):

Heat Equation ◽

Two Dimensional ◽

Random Walkers ◽

Pest Density

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Trapping of biological random walkers Part 1: Predictions for single-trap, multiple-release outcomes based on computer simulations

10.1603/ice.2016.112799 ◽

2016 ◽

Author(s):

James R Miller

Keyword(s):

Computer Simulations ◽

Random Walkers

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Statistical Complexity of Boolean Cellular Automata with Short-Term Reaction-Diffusion Memory on a Square Lattice

Complex Systems ◽

10.25088/complexsystems.28.3.357 ◽

2019 ◽

Vol 28 (3) ◽

pp. 357-391

Author(s):

Zakarya Zarezadeh ◽

Giovanni Costantini ◽

Keyword(s):

Cellular Automata ◽

Reaction Diffusion ◽

Square Lattice ◽

Short Term ◽

Statistical Complexity

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Influence of Flexible Side-Chains on the Breathing Phase Transition of Pillared Layer MOFs: A Force Field Investigation

10.26434/chemrxiv.11720679.v1 ◽

2020 ◽

Author(s):

Julian Keupp ◽

Johannes P. Dürholt ◽

Rochus Schmid

Keyword(s):

First Principles ◽

Good Accuracy ◽

Field Investigation ◽

Square Lattice ◽

Side Chain ◽

Second Step ◽

Side Chains ◽

Dynamics Simulations ◽

Complex Phenomena ◽

Closed Pore

The prototypical pillared layer MOFs, formed by a square lattice of paddle- wheel units and connected by dinitrogen pillars, can undergo a breathing phase transition by a “wine-rack” type motion of the square lattice. We studied this not yet fully understood behavior using an accurate first principles parameterized force field (MOF-FF) for larger nanocrystallites on the example of Zn 2 (bdc) 2 (dabco) [bdc: benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)] and found clear indi- cations for an interface between a closed and an open pore phase traveling through the system during the phase transformation [Adv. Theory Simul. 2019, 2, 11]. In conventional simulations in small supercells this mechanism is prevented by periodic boundary conditions (PBC), enforcing a synchronous transformation of the entire crystal. Here, we extend this investigation to pillared layer MOFs with flexible side-chains, attached to the linker. Such functionalized (fu-)MOFs are experimen- tally known to have different properties with the side-chains acting as fixed guest molecules. First, in order to extend the parameterization for such flexible groups, 1a new parametrization strategy for MOF-FF had to be developed, using a multi- structure force based fit method. The resulting parametrization for a library of fu-MOFs is then validated with respect to a set of reference systems and shows very good accuracy. In the second step, a series of fu-MOFs with increasing side-chain length is studied with respect to the influence of the side-chains on the breathing behavior. For small supercells in PBC a systematic trend of the closed pore volume with the chain length is observed. However, for a nanocrystallite model a distinct interface between a closed and an open pore phase is visible only for the short chain length, whereas for longer chains the interface broadens and a nearly concerted trans- formation is observed. Only by molecular dynamics simulations using accurate force fields such complex phenomena can be studied on a molecular level.

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