arXiv subjects

Ian Morrison

Publications and source records attributed to Ian Morrison.

14 recordsLinked to original sources

arXiv2023

Timing relationships and resulting communications challenges in relativistic travel

Communications to and from a spacecraft undertaking launch-landing interstellar travel at near light speed faces significant challenges. Photon-based communication is significantly impacted by large photon propagation delay and relativistic time dilation. The timing of communications by photon transfer, as measured specifically by local clocks at origin and destination and aboard spacecraft, is analyzed and illustrated for concrete mission scenarios. These include a spacecraft experiencing indefinite constant self-acceleration, and a launch-landing mission, in which a spacecraft experiences constant acceleration for the first half of its cruise phase and a like deceleration for the second half. The origin and destination are assumed to be at rest within a common inertial frame with a wide range of fixed distances separating them. Several typical communication modes are considered, including one-way messaging, two-way message query with an expected response, and the one-way streaming of long program material such as a podcast or video. The local-clock relative timing experienced by the communicating entities including clock images (relation of transmit and receive clocks in one-way communication), the query-response latency (the elapsed time between a query message and reception of a message in response), and the time warping of a streaming program (nonlinear stretching or shrinking of the time axis) are included. In particular, large query-response latency, except for a short interval following launch or before landing, is a severe limit on remote control and social interaction. When photons must travel in the same direction as the spacecraft, communication blackouts strongly limit the periods of time during which communication is possible, and restrict the opportunities for both one-way and two-way communication.

astro-ph.IM↗

arXiv2023

Interstellar flyby scientific data downlink design

The design of a downlink communication system for returning scientific data from an interstellar flyby probe is reviewed in this tutorial white paper. It its assumed that the probe is ballistic, and data is downloaded during a period following encounter with the target star and its exoplanet(s). Performance indices of interest to scientific investigators include the total launch-to-completion data latency and the total volume of data reliably recovered. Issues considered include the interaction between the speed and mass of the probe and the duration of downlink transmission. Optical communication using pulse-position modulation (PPM) with error-correction coding (ECC) is assumed. A very large receiver collection area on or near Earth is composed of individual incoherently-combined diffraction-limited apertures. Other important issues in the design including transmit and receive pointing accuracy and beam size and receiver field of view are reviewed. Numerical examples assume a mission to Proxima Centauri (the nearest star to our Sun) initially launched by directed-energy propulsion from the vicinity of Earth.

astro-ph.IM↗

arXiv2022

Optimal mass and speed for interstellar flyby with directed-energy propulsion

The design of mission scenarios for the flyby investigation of nearby star systems by probes launched using directed energy is addressed. Multiple probes are launched with a fixed launch infrastructure, and download of scientific data occurs following target encounter and data collection. Assuming the primary goal is to reliably recover a larger volume of collected scientific data with a smaller data latency (elapsed time from launch to complete recovery of the data), it is shown that there is an efficient frontier where volume cannot be increased for a given latency and latency cannot be reduced for a given volume. For each probe launch, increasing the volume along this frontier is achieved by increasing the probe mass, which results in a reduced probe speed. Thus choosing the highest feasible probe speed generally does not achieve an efficient tradeoff of volume and latency. Along this frontier the total distance traveled to the completion of data download does not vary significantly, implying that the download time duration is approximately a fixed fraction of the launch-to-target transit time. Due to longer propulsion duration when probe mass is increased, increasing data volume incurs a cost in the total launch energy expended, but with favorable economies of scale. An important characteristic of any probe technology is the scaling law that relates probe mass to transmit data rate, as this affects details of the efficient frontier.

astro-ph.IM↗

arXiv2020

Cyclic Imaging for All-Sky Interference Forecasting with Array Radio Telescopes

Radio Frequency Interference (RFI) is threatening modern radio astronomy. A classic approach to mitigate its impact on astronomical data involves discarding the corrupted time and frequency data samples through a process called flagging and blanking. We propose the exploitation of the cyclostationary properties of the RFI signals to reliably detect and predict their locations within an array radio telescope field-of-view, and dynamically schedule the astronomical observations such as to minimize the probability of RFI data corruption.

eess.SP↗

arXiv2020

Relaying Swarms of Low-Mass Interstellar Probes

Low-mass probes propelled by directed energy from earth are an early option for exploration of nearby star systems. A challenging aspect of such technology is returning scientific observational data to earth. We compare two configurations for achieving this. A direct configuration utilizes optical transmission from the probe to a terrestrial receiver employing a large photon collector. In a relay configuration, probes spaced at uniform intervals act as regenerative repeaters for the scientific data, which eventually arrives at a terrestrial receiver from the most recently launched probe. A number of advantages and disadvantages of the relay configuration are discussed. A numerical comparison approximates equal probe mass in the two cases by using the same optical transmit power and equivalent total transmit plus receive aperture area. When the total downlink data rate is equal, the relay configuration benefits from a smaller terrestrial receive collector, but also requires very frequent launches to achieve higher data rates due to the limitations on relay probe receive aperture area. The direct configuration can achieve higher data rates without such frequent launches by increasing terrestrial collector area. A single-point failure problem in the relay configuration can be addressed by introducing relay-bypass modes, but only at the expense of further increases in launch rate or reductions in data volume, as well as a considerable increase in design and operational complexity. Taking into account launch and collector area costs, the direct configuration is found to achieve lower overall cost by a wide margin over a range of cost parameter values and data rates.

astro-ph.IM↗

arXiv2020

Technological Challenges in Low-mass Interstellar Probe Communication

Building on a preliminary paper design of a downlink from a swarm of low-mass interstellar probes for returning scientific data from the vicinity of Proxima Centauri, the most critical technology issues are summarized, and their significance is explained in the context of the overall system design. The primary goal is to identify major challenges or showstoppers if such a downlink were to be constructed using currently available off-the-shelf technology, and thereby provide direction and motivation to future research on the constituent design challenges and technologies. While there are not any fundamental physical limits that prevent such communication systems, currently available technologies fall significantly short in several areas and there are other major design challenges with uncertain solutions. The greatest identified challenges are in mass constraints, multiplexing simultaneous communication from multiple probes to the same target exoplanet, attitude control and pointing accuracy, and Doppler shifts due to uncertainty in probe velocity. The greatest technology challenges are electrical power, high power and wavelength-agile optical sources, very selective and wavelength-agile banks of optical bandpass filters, and single-photon detectors with extremely low dark-count rates. For a critical subset of these, we describe the nature of the difficulties we encounter and their origins in the overall system context. A receiver that limits reception to a single probe is also considered and compared to the swarm case.

astro-ph.IM↗

arXiv2018

Challenges in Scientific Data Communication from Low-Mass Interstellar Probes

A downlink for the return of scientific data from space probes at interstellar distances is studied. The context is probes moving at relativistic speed using a terrestrial directed-energy beam for propulsion, necessitating very-low mass probes. Achieving simultaneous communication from a swarm of probes launched at regular intervals to a target at the distance of Proxima Centauri is addressed. The analysis focuses on fundamental physical and statistical communication limitations on downlink performance rather than a concrete implementation. Transmission time/distance and probe mass are chosen to achieve the best data latency vs volume tradeoff. Challenges in targeting multiple probe trajectories with a single receiver are addressed, including multiplexing, parallax, and target star proper motion. Relevant sources of background radiation, including cosmic, atmospheric, and receiver dark count are identified and estimated. Direct detection enables high photon efficiency and incoherent aperture combining. A novel burst pulse-position modulation (BPPM) beneficially expands the optical bandwidth and ameliorates receiver dark counts. A canonical receive optical collector combines minimum transmit power with constrained swarm-probe coverage. Theoretical limits on reliable data recovery and sensitivity to the various BPPM model parameters are applied, including a wide range of total collector areas. Significant near-term technological obstacles are identified. Enabling innovations include a high peak-to-average power ratio, a large source extinguishing factor, the shortest atmosphere-transparent wavelength to minimize target star interference, adaptive optics for atmospheric turbulence, very selective bandpass filtering (possibly with multiple passbands), very low dark-count single-photon superconducting detectors, and very accurate attitude control and pointing mechanisms.

astro-ph.IM↗

arXiv2014

Sacks of dice with fair totals

A fair sack is a finite set of independent dice, not required to be fair and allowed to have any number of sides, for which all totals are equally likely. These have been studied for over 60 years. Most results restrict the possible orders of dice in such a sack and almost no examples were known. Building on a rather different approach due to Gasarch and Kruskal, we give an explicit construction of all such sacks.

math.PR↗

arXiv2013

Can you play a fair game of craps with a loaded pair of dice?

We study, in various special cases, total distributions on the product of a finite collection of finite probability spaces and, in particular, the question of when the probability distribution of each factor space is determined by the total distribution.

math.HO↗

arXiv2012

Effective divisors on moduli spaces of curves and abelian varieties

This paper is an expository survey of results about the effective divisors on moduli spaces, with a focus on what is known about the effective cones of moduli spaces of stable curves and of principally polarized abelian varieties. This version incorporates clarifications and suggestions of Ana-Maria Castravet and the referee, both of whom we thank. To appear in the proceedings of the conference, "Joe at 60:A Celebration of Algebraic Geometry" edited by Brendan Hassett, James McKernan, Jason Starr and Ravi Vakil.

math.AG↗

arXiv2009

Groebner techniques for low degree Hilbert stability

We give a method for verifying, by a symbolic calculation, the stability or semistability with respect to a linearization of fixed, possibly small, degree $m$, of the Hilbert point of a scheme $X \in {\mathbb P}(V)$ having a suitably large automorphism group. We also implement our method and apply it to analyze the stability of bicanonical models of certain curves. Our examples are very special, but they arise naturally in the log minimal model program for $\bar{\mathcal M}_g$. In some examples, this connection provides a check of our computations; in others, the computations confirm predictions about conjectural stages of the program.

math.AG↗

arXiv2009

Stability of Tails and 4-Canonical Models

We show that the GIT quotients of suitable loci in the Hilbert and Chow schemes of 4-canonically embedded curves of genus $g\ge 3$ are the moduli space $\bar{M}_g^{\text{ps}}$ of pseudo-stable curves constructed by Schubert in \cite{Schubert} using Chow varieties and 3-canonical models. The only new ingredient needed in the Hilbert scheme variant is a more careful analysis of the stability with respect to a certain 1-ps $λ$ of the $m^{\text{th}}$ Hilbert points of curves $X$ with elliptic tails. We compute the exact weight with which $λ$ acts, and not just the leading term in $m$ of this weight. A similar analysis of stability of curves with rational cuspidal tails allows us to determine the stable and semistable 4-canonical Chow loci. Although here the geometry of the quotient is more complicated because there are strictly semi-stable orbits, we are able to again identify it as $\bar{M}_g^{\text{ps}}$. Our computations yield, as byproducts, examples of both $m$-Hilbert unstable and $m$-Hilbert stable $X$ that are Chow strictly semi-stable.

math.AG↗

arXiv2008

GIT Constructions of Moduli Spaces of Stable Curves and Maps

This largely expository paper first gives an introduction to Hilbert stability and its use in Gieseker's GIT construction of $\overline{M}_g$. Then I review recent work in this area--variants for unpointed curves that arise in Hassett's log minimal model program, starting with Schubert's moduli space of pseudostable curves, and constructions for weighted pointed stable curves and for pointed stable maps due to Swinarski and to Baldwin and Swinarski respectively. The focus is on the steps at which new ideas are needed. Finally, I list open problems in the area, particularly some arising in the log minimal model program that seem inaccessible to current techniques.

math.AG↗

arXiv2001

Towards the ample cone of $\mgn$

In this paper we study the ample cone of the moduli space $\mgn$ of stable $n$-pointed curves of genus $g$. Our motivating conjecture is that a divisor on $\mgn$ is ample iff it has positive intersection with all 1-dimensional strata (the components of the locus of curves with at least $3g+n-2$ nodes). This translates into a simple conjectural description of the cone by linear inequalities, and, as all the 1-strata are rational, includes the conjecture that the Mori cone is polyhedral and generated by rational curves. Our main result is that the conjecture holds iff it holds for $g=0$. More precisely, there is a natural finite map $r: \vmgn 0. 2g+n. \to \mgn$ whose image is the locus $\rgn$ of curves with all components rational. Any 1-strata either lies in $\rgn$ or is numerically equivalent to a family $E$ of elliptic tails and we show that a divisor $D$ is nef iff $D \cdot E \geq 0$ and $r^*(D)$ is nef. We also give results on contractions (i.e. morphisms with connected fibers to projective varieties) of $\mgn$ for $g \geq 1$ showing that any fibration factors through a tautological one (given by forgetting points) and that the exceptional locus of any birational contraction is contained in the boundary. Finally, by more ad-hoc arguments, we prove the nefness of certain special classes.

math.AG↗