arXiv subjects

Blake Wilson

Publications and source records attributed to Blake Wilson.

4 recordsLinked to original sources

arXiv2023

Regulating nanoscale heat transfer with Janus nanoparticles

Janus nanoparticles (JNPs) with heterogeneous compositions or interfacial properties can exhibit directional heating upon external excitation, such as laser radiation and magnetic field. This directional heating may be harnessed for new nanotechnology and biomedical applications. Understanding thermal transport and temperature control with JNP heating is critical for these advances. Here, we developed a numerical framework to analyze the asymmetric thermal transport in JNP heating under photothermal stimulation. We found that JNP-induced temperature contrast, defined as the ratio of temperature increase in the surrounding water, shows a substantial size and polar angle dependence. Notably, we discovered a significant enhancement of the temperature contrast under pulsed heating due to thermal confinement, compared with the continuous heating. This work brings new insights into the thermal responses of JNP heating and advances the field.

physics.app-ph↗

arXiv2022

A Relative Church-Turing-Deutsch Thesis from Special Relativity and Undecidability

Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which begs the question of whether we can prove we exist in a simulation. In this work, we construct a relative model of computation where a computable \textit{local} machine is simulated by a \textit{global}, classical Turing machine. We show that the problem of the local machine computing \textbf{simulation properties} of its global simulator is undecidable in the same sense as the Halting problem. Then, we show that computing the time, space, or error accumulated by the global simulator are simulation properties and therefore are undecidable. These simulation properties give rise to special relativistic effects in the relative model which we use to construct a relative Church-Turing-Deutsch thesis where a global, classical Turing machine computes quantum mechanics for a local machine with the same constant-time local computational complexity as experienced in our universe.

cs.CC↗

arXiv2021

Planning for Package Deliveries in Risky Environments Over Multiple Epochs

We study a risk-aware robot planning problem where a dispatcher must construct a package delivery plan that maximizes the expected reward for a robot delivering packages across multiple epochs. Each package has an associated reward for delivery and a risk of failure. If the robot fails while delivering a package, no future packages can be delivered and the cost of replacing the robot is incurred. The package delivery plan takes place over the course of either a finite or an infinite number of epochs, denoted as the finite horizon problem and infinite horizon problem, respectively. The dispatcher has to weigh the risk and reward of delivering packages during any given epoch against the potential loss of any future epoch's reward. By using the ratio between a package's reward and its risk of failure, we prove an optimal, greedy solution to both the infinite and finite horizon problems. The finite horizon problem can be solved optimally in $O(K n\log n)$ time where $K$ is the number of epochs and $n$ is the number of packages. We show an isomorphism between the infinite horizon problem and Markov Decision Processes to prove an optimal $O(n)$ time algorithm for the infinite horizon problem.

math.OC↗

arXiv2020

Bounds on Sweep-Covers by Raney Numbers

In this work, we introduce a vertex separator in trees known as a sweep-cover that is defined by an ancestor-descendent relationship with all nodes in the tree. We prove the recurrence relation of sweep-covers with $n$ subcovers $P_{\Delta, \gamma}(n)$ on a class of infinite $\Delta$-ary trees with constant path lengths $\gamma$ between the $\Delta$-star internal nodes. Then, we provide recurrence relations for Raney numbers over integer compositions and show that they provide a lower-bound for sweep-covers such that $P_{\Delta, \gamma}(n) = \Omega\left( \frac{\sqrt{2 \pi} n^{\Delta n + \Delta + \frac{3}{2}}}{e^n ((\Delta-1)n+\Delta+1)!(n+1)!} \gamma \right)$.

math.CO↗