arXiv subjects

Calvin Pozderac

Publications and source records attributed to Calvin Pozderac.

5 recordsLinked to original sources

arXiv2025

The benefit of ignorance for traffic through a random congestible network

When traffic is routed through a network that is susceptible to congestion, the self-interested decisions made by individual users do not, in general, produce the optimal flow. This discrepancy is quantified by the so-called "price of anarchy." Here we consider whether the traffic produced by self-interested users is made better or worse when users have uncertain knowledge about the cost functions of the links in the network, and we define a parallel concept that we call the "price of ignorance." We introduce a simple model in which fast, congestible links and slow, incongestible links are mixed randomly in a large network and users plan their routes with finite uncertainty about which of the two cost functions describes each link. One of our key findings is that a small level of user ignorance universally improves traffic, regardless of the network composition. Further, there is an optimal level of ignorance which, in our model, causes the self-interested user behavior to coincide with the optimum. Many features of our model can be understood analytically, including the optimal level of user ignorance and the existence of critical scaling near the percolation threshold for fast links, where the potential benefit of user ignorance is greatest.

cond-mat.dis-nn↗

arXiv2023

Two-dimensional hydrodynamic electron flow through periodic and random potentials

We study the hydrodynamic flow of electrons through a smooth potential energy landscape in two dimensions, for which the electrical current is concentrated along thin channels that follow percolating equipotential contours. The width of these channels, and hence the electrical resistance, is determined by a competition between viscous and thermoelectric forces. For the case of periodic (moir\'{e}) potentials, we find that hydrodynamic flow provides a new route to linear-in-$T$ resistivity. We calculate the associated prefactors for potentials with $C_3$ and $C_4$ symmetry. On the other hand, for a random potential the resistivity has qualitatively different behavior because equipotential paths become increasingly tortuous as their width is reduced. This effect leads to a resistivity that grows with temperature as $T^{10/3}$.

cond-mat.str-el↗

arXiv2022

Exact solution for the filling-induced thermalization transition in a 1D fracton system

We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system exhibits a continuous phase transition between a weakly fragmented ("thermalizing") phase and a strongly fragmented ("nonthermalizing") phase as a function of the number density of particles. Here, by mapping to two different problems in combinatorics, we identify an exact solution for the critical density $n_c$. Specifically, when evolution proceeds by operators that act on $\ell$ contiguous sites, the critical density is given by $n_c = 1/(\ell -2)$. We identify the critical scaling near the transition, and we show that there is a universal value of the correlation length exponent $ν= 2$. We confirm our theoretical results with numeric simulations. In the thermalizing phase the dynamical exponent is subdiffusive: $z=4$, while at the critical point it increases to $z_c \gtrsim 6$.

cond-mat.stat-mech↗

arXiv2021

Relation between Johnson Noise and heating power in a two-terminal conductor

We consider the Johnson noise of a two-dimensional, two-terminal electrical conductor for which the electron system obeys the Wiedemann-Franz law. We derive two simple and generic relations between the Johnson Noise temperature and the heat flux into the electron system. First, we consider the case where the electron system is heated by Joule heating from a DC current, and we show that there is a universal proportionality coefficient between the Joule power and the increase in Johnson noise temperature. Second, we consider the case where heat flows into the sample from an external source, and we derive a simple relation between the Johnson noise temperature and the heat flux across the boundary of the sample.

cond-mat.mes-hall↗

arXiv2021

Superspreading of SARS-CoV-2 in the USA

A number of epidemics, including the SARS-CoV-1 epidemic of 2002-2004, have been known to exhibit superspreading, in which a small fraction of infected individuals is responsible for the majority of new infections. The existence of superspreading implies a fat-tailed distribution of infectiousness (new secondary infections caused per day) among different individuals. Here, we present a simple method to estimate the variation in infectiousness by examining the variation in early-time growth rates of new cases among different subpopulations. We use this method to estimate the mean and variance in the infectiousness, $β$, for SARS-CoV-2 transmission during the early stages of the pandemic within the United States. We find that $σ_β/μ_β\gtrsim 3.2$, where $μ_β$ is the mean infectiousness and $σ_β$ its standard deviation, which implies pervasive superspreading. This result allows us to estimate that in the early stages of the pandemic in the USA, over 81% of new cases were a result of the top 10% of most infectious individuals.

q-bio.PE↗