arXiv subjects

Richard Price

Publications and source records attributed to Richard Price.

At least 19 recordsLinked to original sources

arXiv2025

Lifetime-Aware Design for Item-Level Intelligence at the Extreme Edge

We present FlexiFlow, a lifetime-aware design framework for item-level intelligence (ILI) where computation is integrated directly into disposable products like food packaging and medical patches. Our framework leverages natively flexible electronics which offer significantly lower costs than silicon but are limited to kHz speeds and several thousands of gates. Our insight is that unlike traditional computing with more uniform deployment patterns, ILI applications exhibit 1000X variation in operational lifetime, fundamentally changing optimal architectural design decisions when considering trillion-item deployment scales. To enable holistic design and optimization, we model the trade-offs between embodied carbon footprint and operational carbon footprint based on application-specific lifetimes. The framework includes: (1) FlexiBench, a workload suite targeting sustainability applications from spoilage detection to health monitoring; (2) FlexiBits, area-optimized RISC-V cores with 1/4/8-bit datapaths achieving 2.65X to 3.50X better energy efficiency per workload execution; and (3) a carbon-aware model that selects optimal architectures based on deployment characteristics. We show that lifetime-aware microarchitectural design can reduce carbon footprint by 1.62X, while algorithmic decisions can reduce carbon footprint by 14.5X. We validate our approach through the first tape-out using a PDK for flexible electronics with fully open-source tools, achieving 30.9kHz operation. FlexiFlow enables exploration of computing at the Extreme Edge where conventional design methodologies must be reevaluated to account for new constraints and considerations.

cs.AR↗

arXiv2023

Angular Momentum for Black Hole Binaries in Numerical Relativity

The extensive catalog of waveforms, with details of binary black hole inspiral and merger, offer an opportunity to understand black hole interactions beyond the large separation regime. We envision a research program that focuses on the transfer of angular momentum from spin of the individual holes to the orbital angular momentum and the role of tidal coupling in the process. That analysis will require the formulation of an expression for the orbital angular momentum of a binary, an expression that is useful at small separations, since that regime is well out of the range of Newtonian approximations and is where tidal coupling should be most interesting. We report here such an expression, a binary orbital angular momentum based on numerical relativity results for quasi-circular orbits, that agrees remarkably well with a similar quantity constructed with particle-perturbation techniques for the Kerr geometry.

gr-qc↗

arXiv2022

Issues in the comparison of particle perturbations and numerical relativity for binary black hole mergers

Recent work on improved efficiency of calculations for extreme mass ratio inspirals has produced the useful byproduct of comparisons of inspirals of comparable mass by particle perturbation (PP) methods and by numerical relativty (NR). Here we point out: (1) In choosing the rescaling of the masses, consideration must be given to the differences in the PP and NR methods even in the earliest, least nonlinear regime; in particular barycenter effects must be addressed. (2) Care must be given to the comparison of the nonspinning remnant in PP and the rapidly spinning remnant in NR.

gr-qc↗

arXiv2017

Closed Timelike Curves and "Effective" Superluminal Travel with Naked Line Singularities

We examine closed timelike curves (CTCs) and "effective" superluminal travel in a spacetime containing naked line singularities, which we call "wires". Each wire may be straight-line singularity or a ring singularity. The Weak Energy Condition (WEC) is preserved in all well-defined regions of the spacetime. (The singularities themselves are not well-defined, so the WEC is undefined there, but it is never explicitly violated.) Parallel to the wire, "effective" superluminal travel is possible, in that the wire may be used as a shortcut between distant regions of spacetime. Our purpose in presenting the superluminal aspects of the wire is to dispel the commonly held view that explicit WEC violation is necessary for effective superluminal travel, whereas in truth the strictures against superluminal travel are more complicated. We also demonstrate how the existence of such "wires" could create CTCs. We present a model spacetime which contains two wires which are free to move relative to each other. This spacetime is asymptotically flat: It becomes a Minkowski spacetime a finite distance away from each of the wires. The CTCs under investigation do not need to enter the wires' singularities, and can be confined to regions that are weak-field: This means that if these wires were physically possible, they would present causality problems even in nonsingular, energetically realistic regions of the spacetime. We conclude that the Weak Energy Condition alone is not sufficient to prevent superluminal travel in asymptotically flat spacetimes.

gr-qc↗

arXiv2017

Scalar Fields in Black Hole Spacetimes

The time-evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime, has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, time-like infinity and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index $\ell$ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.

gr-qc↗

arXiv2017

Gravitational wave sources: reflections and echoes

The recent detection of gravitational waves has generated interest in alternatives to the black hole interpretation of sources. One set of such alternatives involves a prediction of gravitational wave "echoes". We consider two aspects of possible echoes: First, general features of echoes coming from spacetime reflecting conditions. We find that the detailed nature of such echoes does not bear any clear relationship to quasi-normal frequencies. Second, we point out the pitfalls in the analysis of local reflecting "walls" near the horizon of rapidly rotating black holes.

gr-qc↗

arXiv2007

Two-timescale adiabatic expansion of a scalar field model

The analysis of gravitational wave data may require greater accuracy than is afforded by the adiabatic approximation to the trajectory of and field produced by a particle moving in curved spacetime. Higher accuracy is available with a two-timescale approach using as an expansion parameter the ratio of orbital time to radiation reaction time. To avoid apparent divergences at large distances, the details of the method are important, especially the choice of the foliation, the spacetime surfaces on which the orbital elements are taken to be constant. Here we apply the two-timescale approach to a simple linear model to demonstrate the details of the method. In particular we use it to show that a null foliation avoids large-distance divergences in the first-order post-adiabatic approximation, and we argue that this will be true more generally for a null foliation.

gr-qc↗

arXiv2000

Quasi-stationary binary inspiral II: Radiation-balanced boundary conditions

The quasi-stationary method for black hole binary inspiral is an approximation for studying strong field effects while suppressing radiation reaction. In this paper we use a nonlinear scalar field toy model (i) to explain the underlying method of approximating binary motion by periodic orbits with radiation; (ii) to show how the fields in such a model are found by the solution of a boundary value problem; (iii) to demonstrate how a good approximation to the outgoing radiation can be found by finding fields with a balance of ingoing and outgoing radiation (a generalization of standing waves).

gr-qc↗

arXiv2000

Close limit of grazing black hole collisions: non-spinning holes

Using approximate techniques we study the final moments of the collision of two (individually non-spinnning) black holes which inspiral into each other. The approximation is based on treating the whole space-time as a single distorted black hole. We obtain estimates for the radiated energy, angular momentum and waveforms for the gravitational waves produced in such a collision. The results can be of interest for analyzing the data that will be forthcoming from gravitational wave interferometric detectors, like the LIGO, GEO, LISA, VIRGO and TAMA projects.

gr-qc↗

arXiv1999

Inspiralling black holes: the close limit

Using several approximations, we calculate an estimate of the gravitational radiation emitted when two equal mass black holes coalesce at the end of their binary inspiral. We find that about 1% of the mass energy of the pair will emerge as gravitational waves during the final ringdown and a negligible fraction of the angular momentum will be radiated.

gr-qc↗

arXiv1998

Gravitational radiation from Schwarzschild black holes: the second order perturbation formalism

The perturbation theory of black holes has been useful recently for providing estimates of gravitational radiation from black hole collisions. Second order perturbation theory, relatively undeveloped until recently, has proved to be important both for providing refined estimates and for indicating the range of validity of perturbation theory. Here we present the second order formalism for perturbations of Schwarzschild spacetimes. The emphasis is on practical methods for carrying out second order computations of outgoing radiation. General issues are illustrated throughout with examples from ``close-limit'' results, perturbation calculations in which black holes start from small separation.

gr-qc↗

arXiv1998

The collision of boosted black holes: second order close limit calculations

We study the head-on collision of black holes starting from unsymmetrized, Brill--Lindquist type data for black holes with non-vanishing initial linear momentum. Evolution of the initial data is carried out with the ``close limit approximation,'' in which small initial separation and momentum are assumed, and second-order perturbation theory is used. We find agreement that is remarkably good, and that in some ways improves with increasing momentum. This work extends a previous study in which second order perturbation calculations were used for momentarily stationary initial data, and another study in which linearized perturbation theory was used for initially moving holes. In addition to supplying answers about the collisions, the present work has revealed several subtle points about the use of higher order perturbation theory, points that did not arise in the previous studies. These points include issues of normalization, and of comparison with numerical simulations, and will be important to subsequent applications of approximation methods for collisions.

gr-qc↗

arXiv1997

Evolving the Bowen-York initial data for spinning black holes

The Bowen-York initial value data typically used in numerical relativity to represent spinning black hole are not those of a constant-time slice of the Kerr spacetime. If Bowen-York initial data are used for each black hole in a collision, the emitted radiation will be partially due to the ``relaxation'' of the individual holes to Kerr form. We compute this radiation by treating the geometry for a single hole as a perturbation of a Schwarzschild black hole, and by using second order perturbation theory. We discuss the extent to which Bowen-York data can be expected accurately to represent Kerr holes.

gr-qc↗

arXiv1997

A slightly less grand challenge: Colliding Black Holes using perturbation techniques

Perturbation techniques can be used as an alternative to supercomputer calculations in calculating gravitational radiation emitted by colliding black holes, provided the process starts with the black holes close to each other. We give a summary of the method and of the results obtained for various initial configurations, both axisymmetric and without symmetry: Initially static, boosted towards each other, counter-rotating, or boosted at an angle (pseudo-inspiral). Where applicable, we compare the perturbation results with supercomputer calculations.

gr-qc↗

arXiv1996

Head-on collision of unequal mass black holes: close-limit predictions

The close-limit method has given approximations in excellent agreement with those of numerical relativity for collisions of equal mass black holes. We consider here colliding holes with unequal mass, for which numerical relativity results are not available. We try to ask two questions: (i) Can we get approximate answers to astrophysical questions (ideal mass ratio for energy production, maximum recoil velocity, etc.), and (ii) can we better understand the limitations of approximation methods. There is some success in answering the first type of question, but more with the second, especially in connection with the issue of measures of the intrinsic mass of the colliding holes, and of the range of validity of the method.

gr-qc↗

arXiv1996

Colliding black holes: how far can the close approximation go?

We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed waveforms and energy. Much more important, second-order results correctly indicate the range of validity of perturbation theory. This use of second-order, to provide ``error bars,'' makes perturbation theory a viable tool for providing benchmarks for numerical relativity in more generic collisions and, in some range of collision parameters, for supplying waveform templates for gravitational wave detection.

gr-qc↗

arXiv1996

The collision of boosted black holes

We study the radiation from a collision of black holes with equal and opposite linear momenta. Results are presented from a full numerical relativity treatment and are compared with the results from a ``close-slow'' approximation. The agreement is remarkable, and suggests several insights about the generation of gravitational radiation in black hole collisions.

gr-qc↗

arXiv1996

Second order perturbations of a Schwarzschild black hole

We study the even-parity $\ell=2$ perturbations of a Schwarzschild black hole to second order. The Einstein equations can be reduced to a single linear wave equation with a potential and a source term. The source term is quadratic in terms of the first order perturbations. This provides a formalism to address the validity of many first order calculations of interest in astrophysics.

gr-qc↗