arXiv subjects

S. Redner

Publications and source records attributed to S. Redner.

At least 37 records · Page 2Linked to original sources

arXiv2022

First-Passage-Driven Boundary Recession

We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically rich dynamics arises. In particular, the probability for the particle to first reach the moving boundary for the $n^\text{th}$ time asymptotically scales as $t^{-(1+2^{-n})}$. Because the tail of this distribution becomes progressively fatter, the typical time between successive first passages systematically gets longer. We also find that the number of collisions between the particle and the boundary scales as $\ln\ln t$, while the time dependence of the boundary position varies as $t/\ln t$.

cond-mat.stat-mech↗

arXiv2022

Fixation and Fluctuations in Two-Species Cooperation

Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are driven by cooperative and symmetric interactions between these species. For an isolated population, we determine the probability to reach fixation, where only one species remains, as a function of the initial concentrations of the two species, as well as the time to reach fixation. The latter scales exponentially with the population size. When members of each species migrate into the population at rate $λ$ and replace a randomly selected individual, surprisingly rich dynamics ensues. Ostensibly, the population reaches a steady state, but the steady-state population distribution undergoes a unimodal to trimodal transition as the migration rate decreases below a critical value $λ_c$. In the low-migration regime, $λ<λ_c$, the steady state is not truly steady, but instead strongly fluctuates between near-fixation states, where the population consists of mostly A's or of mostly B's. The characteristic time scale of these fluctuations diverges as $λ^{-1}$. Thus in spite of the cooperative interaction, a typical snapshot of the population will contain almost all A's or almost all B's.

q-bio.PE↗

arXiv2022

How Smart Should a Forager Be?

We introduce an idealized model of an intelligent forager in which higher intelligence corresponds to a larger spatial range over which the forager can detect food. Such a forager diffuses randomly whenever the nearest food is more distant than the forager's detection range, $R$, and moves ballistically towards the nearest food inside its detection range. Concomitantly, the forager's metabolic energy cost per step is an increasing function of its intelligence. A dumb forager wanders randomly and may miss nearby food, thus making it susceptible to starvation. Conversely, a too-smart forager incurs a large metabolic cost per step during its search for food and is again susceptible to starvation. We show that the forager's lifetime is maximized at an optimal, intermediate level of intelligence.

physics.bio-ph↗

arXiv2021

A Tale of Two (and More) Altruists

We introduce a minimalist dynamical model of wealth evolution and wealth sharing among $N$ agents as a platform to compare the relative merits of altruism and individualism. In our model, the wealth of each agent independently evolves by diffusion. For a population of altruists, whenever any agent reaches zero wealth (that is, the agent goes bankrupt), the remaining wealth of the other $N-1$ agents is equally shared among all. The population is collectively defined to be bankrupt when its total wealth falls below a specified small threshold value. For individualists, each time an agent goes bankrupt (s)he is considered to be "dead" and no wealth redistribution occurs. We determine the evolution of wealth in these two societies. Altruism leads to more global median wealth at early times; eventually, however, the longest-lived individualists accumulate most of the wealth and are richer and more long lived than the altruists.

physics.soc-ph↗

arXiv2021

Divergence and Consensus in Majority Rule

We investigate majority rule dynamics in a population with two classes of people, each with two opinion states $\pm 1$, and with tunable interactions between people in different classes. In an update, a randomly selected group adopts the majority opinion if all group members belong to the same class; if not, majority rule is applied with probability $ε$. Consensus is achieved in a time that scales logarithmically with population size if $ε\geq ε_c=\frac{1}{9}$. For $ε<ε_c$, the population can get trapped in a polarized state, with one class preferring the $+1$ state and the other preferring $-1$. The time to escape this polarized state and reach consensus scales exponentially with population size.

cond-mat.stat-mech↗

arXiv2021

Immortal Branching Processes

We introduce and study the dynamics of an \emph{immortal} critical branching process. In the classic, critical branching process, particles give birth to a single offspring or die at the same rates. Even though the average population is constant in time, the ultimate fate of the population is extinction. We augment this branching process with immortality by positing that either: (a) a single particle cannot die, or (b) there exists an immortal stem cell that gives birth to ordinary cells that can subsequently undergo critical branching. We discuss the new dynamical aspects of this immortal branching process.

math.PR↗

arXiv2020

When Will an Elevator Arrive?

We present and analyze a minimalist model for the vertical transport of people in a tall building by elevators. We focus on start-of-day operation in which people arrive at the ground floor of the building at a fixed rate. When an elevator arrives on the ground floor, passengers enter until the elevator capacity is reached, and then they are transported to their destination floors. We determine the distribution of times that each person waits until an elevator arrives, the number of people waiting for elevators, and transition to synchrony for multiple elevators when the arrival rate of people is sufficiently large. We validate many of our predictions by event-driven simulations.

cond-mat.stat-mech↗

arXiv2020

Optimization and Growth in First-Passage Resetting

We combine the processes of resetting and first-passage to define \emph{first-passage resetting}, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. In an infinite domain, first-passage resetting of isotropic diffusion is non-stationary, with the number of resetting events growing with time as $\sqrt{t}$. We calculate the resulting spatial probability distribution of the particle analytically, and also obtain this distribution by a geometric path decomposition. In a finite interval, we define an optimization problem that is controlled by first-passage resetting; this scenario is motivated by reliability theory. The goal is to operate a system close to its maximum capacity without experiencing too many breakdowns. However, when a breakdown occurs the system is reset to its minimal operating point. We define and optimize an objective function that maximizes the reward (being close to maximum operation) minus a penalty for each breakdown. We also investigate extensions of this basic model to include delay after each reset and to two dimensions. Finally, we study the growth dynamics of a domain in which the domain boundary recedes by a specified amount whenever the diffusing particle reaches the boundary after which a resetting event occurs. We determine the growth rate of the domain for the semi-infinite line and the finite interval and find a wide range of behaviors that depend on how much the recession occurs when the particle hits the boundary.

cond-mat.stat-mech↗

arXiv2020

Optimization in First-Passage Resetting

We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability distribution exhibits rich features. In a finite domain, we define a non-trivial optimization in which a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset point. We derive the condition to optimize the net gain in this system, namely, the reward minus the cost.

cond-mat.stat-mech↗

arXiv2020

Where Should You Park Your Car? The $\frac{1}{2}$ Rule

We investigate parking in a one-dimensional lot, where cars enter at a rate $λ$ and each attempts to park close to a target at the origin. Parked cars also depart at rate 1. An entering driver cannot see beyond the parked cars for more desirable open spots. We analyze a class of strategies in which a driver ignores open spots beyond $τL$, where $τ$ is a risk threshold and $L$ is the location of the most distant parked car, and attempts to park at the first available spot encountered closer than $τL$. When all drivers use this strategy, the probability to park at the best available spot is maximal when $τ=\frac{1}{2}$, and parking at the best available spot occurs with probability $\frac{1}{4}$.

physics.soc-ph↗

arXiv2020

Simple Parking Strategies

We investigate simple strategies that embody the decisions that one faces when trying to park near a popular destination. Should one park far from the target (destination), where finding a spot is easy, but then be faced with a long walk, or should one attempt to look for a desirable spot close to the target, where spots may be hard to find? We study an idealized parking process on a one-dimensional geometry where the desired target is located at $x=0$, cars enter the system from the right at a rate $λ$ and each car leaves at a unit rate. We analyze three parking strategies---meek, prudent, and optimistic---and determine which is optimal.

physics.soc-ph↗

arXiv2019

Polarization and Consensus by Opposing External Sources

We introduce a socially motivated extension of the voter model in which individual voters are also influenced by two opposing, fixed-opinion news sources. These sources forestall consensus and instead drive the population to a politically polarized state, with roughly half the population in each opinion state. Two types social networks for the voters are studied: (a) the complete graph of $N$ voters and, more realistically, (b) the two-clique graph with $N$ voters in each clique. For the complete graph, many dynamical properties are soluble within an annealed-link approximation, in which a link between a news source and a voter is replaced by an average link density. In this approximation, we show that the average consensus time grows as $N^α$, with $α= p\ell/(1-p)$. Here $p$ is the probability that a voter consults a news source rather than a neighboring voter, and $\ell$ is the link density between a news source and voters, so that $α$ can be greater than 1. The polarization time, namely, the time to reach a politically polarized state from an initial strong majority state, is typically much less than the consensus time. For voters on the two-clique graph, either reducing the density of interclique links or enhancing the influence of news sources again promotes polarization.

physics.soc-ph↗

arXiv2019

Opinion Formation under Antagonistic Influences

We study the opinion dynamics in a generalized voter model in which voters are additionally influenced by two antagonistic news sources, whose effect is to promote political polarization. We show that, as the influence of the news sources is increased, the mean time to reach consensus is anomalously long, the time to reach a politically polarized state is quite short, and the steady-state opinion distribution exhibits a transition from a near consensus state to a politically polarized state.

physics.soc-ph↗

arXiv2019

Fixation in Fluctuating Populations

We investigate the dynamics of the voter model in which the population itself changes endogenously via the birth-death process. There are two species of voters, labeled A and B, and the population of each species can grow or shrink by the birth-death process at equal rates $b$. Individuals of opposite species also undergo voter model dynamics in which an AB pair can equiprobably become AA or BB with rate $v$---neutral evolution. In the limit $b/v\to\infty$, the distribution of consensus times varies as $t^{-3}$ and the probability that the population size equals $n$ at the moment of consensus varies as $n^{-3}$. As the birth/death rate $b$ is increased, fixation occurs more more quickly; that is, population fluctuations promote consensus.

q-bio.PE↗

arXiv2019

Exclusion in Junction Geometries

We investigate the dynamics of the asymmetric exclusion process at a junction. When two input roads are initially fully occupied and a single output road is initially empty, the ensuing rarefaction wave has a rich spatial structure. The density profile also changes dramatically as the initial densities are varied. Related phenomenology arises when one road feeds into two. Finally, we determine the phase diagram of the open system, where particles are fed into two roads at rate $α$ for each road, the two roads merge into one, and particles are extracted from the single output road at rate $β$.

cond-mat.stat-mech↗

arXiv2019

Topology Controlled Potts Coarsening

We uncover unusual topological features in the long-time relaxation of the $q$-state kinetic Potts ferromagnet on the triangular lattice that is instantaneously quenched to zero temperature from a zero-magnetization initial state. For $q=3$, the final state is either: the ground state (frequency $\approx 0.75$), a frozen three-hexagon state (frequency $\approx 0.16$), a two-stripe state (frequency $\approx 0.09$), or a three-stripe state (frequency $<2\times 10^{-4}$). Other final state topologies, such as states with more than 3 hexagons, occur with probability $10^{-5}$ or smaller, for $q=3$. The relaxation to the frozen three-hexagon state is governed by a time that scales as $L^2\ln L$. We provide a heuristic argument for this anomalous scaling and present additional new features of Potts coarsening on the triangular lattice for $q=3$ and for $q>3$.

cond-mat.stat-mech↗

arXiv2019

Reputation-Driven Voting Dynamics

We introduce the reputational voter model (RVM) to account for the time-varying abilities of individuals to influence their neighbors. To understand of the RVM, we first discuss the fitness voter model (FVM), in which each voter has a fixed and distinct fitness. In a voting event where voter $i$ is fitter than voter $j$, only $j$ changes opinion. We show that the dynamics of the FVM and the voter model are identical. We next discuss the adaptive voter model (AVM), in which the influencing voter in a voting event increases its fitness by a fixed amount. The dynamics of the AVM is non-stationary and slowly crosses over to that of FVM because of the gradual broadening of the fitness distribution of the population. Finally, we treat the RVM, in which the voter $i$ is endowed with a reputational rank $r_i$ that ranges from 1 (highest rank) to $N$ (lowest), where $N$ is the population size. In a voting event in which voter $i$ outranks $j$, only the opinion of $j$ changes. Concomitantly, the rank of $i$ increases, while that of $j$ does not change. The rank distribution remains uniform on the integers $1,2,3,\ldots,N$, leading to stationary dynamics. For equal number of voters in the two voting states with these two subpopulations having the same average rand, the time to reach consensus in the mean-field limit scales as $\exp(\sqrt{N})$. This long consensus time arises because the average rank of the minority population is typically higher than that of the majority. Thus whenever consensus is approached, this highly ranked minority tends to drive the population away from consensus.

physics.soc-ph↗

arXiv2019

Reality Inspired Voter Models: A Mini-Review

This mini-review presents extensions of the voter model that incorporate various plausible features of real decision-making processes by individuals. Although these generalizations are not calibrated by empirical data, the resulting dynamics are suggestive of realistic collective social behaviors.

physics.soc-ph↗