skip to main content


Title: Multifractality of light in photonic arrays based on algebraic number theory
Abstract

Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity that is mathematically described by fractal geometry. Here, we extend the reach of fractal concepts in photonics by experimentally demonstrating multifractality of light in arrays of dielectric nanoparticles that are based on fundamental structures of algebraic number theory. Specifically, we engineered novel deterministic photonic platforms based on the aperiodic distributions of primes and irreducible elements in complex quadratic and quaternions rings. Our findings stimulate fundamental questions on the nature of transport and localization of wave excitations in deterministic media with multi-scale fluctuations beyond what is possible in traditional fractal systems. Moreover, our approach establishes structure–property relationships that can readily be transferred to planar semiconductor electronics and to artificial atomic lattices, enabling the exploration of novel quantum phases and many-body effects.

 
more » « less
Award ID(s):
1709704
NSF-PAR ID:
10159525
Author(s) / Creator(s):
; ; ; ; ;
Publisher / Repository:
Nature Publishing Group
Date Published:
Journal Name:
Communications Physics
Volume:
3
Issue:
1
ISSN:
2399-3650
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Investigating the nature of system intrusions in large distributed systems remains a notoriously difficult challenge. While monitoring tools (e.g., Firewalls, IDS) provide preliminary alerts through easy-to-use administrative interfaces, attack reconstruction still requires that administrators sift through gigabytes of system audit logs stored locally on hundreds of machines. At present, two fundamental obstacles prevent synergy between system-layer auditing and modern cluster monitoring tools: 1) the sheer volume of audit data generated in a data center is prohibitively costly to transmit to a central node, and 2) system- layer auditing poses a “needle-in-a-haystack” problem, such that hundreds of employee hours may be required to diagnose a single intrusion. This paper presents Winnower, a scalable system for audit-based cluster monitoring that addresses these challenges. Our key insight is that, for tasks that are replicated across nodes in a distributed application, a model can be defined over audit logs to succinctly summarize the behavior of many nodes, thus eliminating the need to transmit redundant audit records to a central monitoring node. Specifically, Winnower parses audit records into provenance graphs that describe the actions of individual nodes, then performs grammatical inference over individual graphs using a novel adaptation of Deterministic Finite Automata (DFA) Learning to produce a behavioral model of many nodes at once. This provenance model can be efficiently transmitted to a central node and used to identify anomalous events in the cluster. We have implemented Winnower for Docker Swarm container clusters and evaluate our system against real-world applications and attacks. We show that Winnower dramatically reduces storage and network overhead associated with aggregating system audit logs, by as much as 98%, without sacrificing the important information needed for attack investigation. Winnower thus represents a significant step forward for security monitoring in distributed systems. 
    more » « less
  2. There has been a flurry of recent literature studying streaming algorithms for which the input stream is chosen adaptively by a black-box adversary who observes the output of the streaming algorithm at each time step. However, these algorithms fail when the adversary has access to the internal state of the algorithm, rather than just the output of the algorithm. We study streaming algorithms in the white-box adversarial model, where the stream is chosen adaptively by an adversary who observes the entire internal state of the algorithm at each time step. We show that nontrivial algorithms are still possible. We first give a randomized algorithm for the L1-heavy hitters problem that outperforms the optimal deterministic Misra-Gries algorithm on long streams. If the white-box adversary is computationally bounded, we use cryptographic techniques to reduce the memory of our L1-heavy hitters algorithm even further and to design a number of additional algorithms for graph, string, and linear algebra problems. The existence of such algorithms is surprising, as the streaming algorithm does not even have a secret key in this model, i.e., its state is entirely known to the adversary. One algorithm we design is for estimating the number of distinct elements in a stream with insertions and deletions achieving a multiplicative approximation and sublinear space; such an algorithm is impossible for deterministic algorithms. We also give a general technique that translates any two-player deterministic communication lower bound to a lower bound for randomized algorithms robust to a white-box adversary. In particular, our results show that for all p ≥ 0, there exists a constant Cp > 1 such that any Cp-approximation algorithm for Fp moment estimation in insertion-only streams with a white-box adversary requires Ω(n) space for a universe of size n. Similarly, there is a constant C > 1 such that any C-approximation algorithm in an insertion-only stream for matrix rank requires Ω(n) space with a white-box adversary. These results do not contradict our upper bounds since they assume the adversary has unbounded computational power. Our algorithmic results based on cryptography thus show a separation between computationally bounded and unbounded adversaries. Finally, we prove a lower bound of Ω(log n) bits for the fundamental problem of deterministic approximate counting in a stream of 0’s and 1’s, which holds even if we know how many total stream updates we have seen so far at each point in the stream. Such a lower bound for approximate counting with additional information was previously unknown, and in our context, it shows a separation between multiplayer deterministic maximum communication and the white-box space complexity of a streaming algorithm 
    more » « less
  3. Abstract

    This article investigates the resonant behavior of a novel family of fractal boundary antennas at the fundamental mode of operation. The miniaturization patterns over iterations as well as over the number of segments on the boundary have been studied by simulating the fractal antennas in High Frequency Structure Simulator (HFSS). The antennas are fed by a 50‐Ω coaxial probe, which is placed at the best position on the patch, with impedance matching andS11< −10 dB. Analysis of the resonant frequency with respect to the square‐shaped fractal generator resulted in curve‐fit expressions that vary with a single variable of either iteration or number of segments on the boundary. The derived equations are independent from the substrate thickness. They are useful to design miniature patch antennas within a specified area in order to resonate at a desired frequency by simply changing the boundary or the fractal iteration.

     
    more » « less
  4. Abstract

    Black carbon aerosol emissions are recognized as contributors to global warming and air pollution. There remains, however, a lack of techniques to remotely measure black carbon aerosol particles with high range and time resolution. This article presents a direct and contact-free remote technique to estimate the black carbon aerosol number and mass concentration at a few meters from the emission source. This is done using the Colibri instrument based on a novel technique, referred to here as Picosecond Short-Range Elastic Backscatter Lidar (PSR-EBL). To address the complexity of retrieving lidar products at short measurement ranges, we apply a forward inversion method featuring radiometric lidar calibration. Our method is based on an extension of a well-established light-scattering model, the Rayleigh–Debye–Gans for Fractal-Aggregates (RDG-FA) theory, which computes an analytical expression of lidar parameters. These parameters are the backscattering cross-sections and the lidar ratio for black carbon fractal aggregates. Using a small-scale Jet A-1 kerosene pool fire, we demonstrate the ability of the technique to quantify the aerosol number and mass concentration with centimetre range-resolution and millisecond time-resolution.

     
    more » « less
  5. Abstract

    Ecological studies of global warming impacts have many constraints. Organisms are often exposed to higher temperatures for short periods of time, probably underestimating their ability to acclimate or adapt relative to slower but real rates of warming. Many studies also focus on a limited number of traits and miss the multifaceted effects that warming may have on organisms, from physiology to behaviour. Organisms exhibit different movement traits, some of which are primarily driven by metabolic processes and others by decision‐making, which should influence the extent to which temperature affects them.

    We collected snails from streams that have been differentially heated by geothermal activity for decades to determine how long‐term exposure to different temperatures affected their metabolism and movement. Additionally, we collected snails from a cold stream (5°C) and measured their metabolism and movement at higher temperatures (short‐term exposure). We used respirometry to measure metabolic rates and automated in situ image‐based tracking to quantify several movement traits from 5 to 21°C.

    Long‐term exposure to higher temperatures resulted in a greater thermal sensitivity of metabolic rate compared to snails exposed for short durations, highlighting the need for caution when conducting acute temperature exposures in global warming research. Average speed, which is largely driven by metabolism, also increased more with temperature for long‐term exposure compared to short‐term exposure. Movement traits we interpret as more decision‐based, such as time spent moving and trajectory shape, were less affected by temperature. Step length increased and step angle decreased at higher temperatures for both long‐ and short‐term exposure, resulting in overall straighter trajectories. The power‐law exponent of the step length distributions and fractal dimension of trajectories were independent of temperature, however, suggesting that snails retained the same movement strategy.

    The observed changes in snail movement at higher temperatures should lead to higher encounter rates and more efficient searching, providing a behavioural mechanism for stronger plant–herbivore interactions in warmer environments. Our research is among the first to show that temperature has contrasting effects on different movement traits, which may be determined by the metabolic contribution to those behaviours.

     
    more » « less