skip to main content

Explore Research Products in the NSF-PAR

Title: Hydrodynamic effective field theories with discrete rotational symmetry
A bstract We develop a hydrodynamic effective field theory on the Schwinger-Keldysh contour for fluids with charge, energy, and momentum conservation, but only discrete rotational symmetry. The consequences of anisotropy on thermodynamics and first-order dissipative hydrodynamics are detailed in some simple examples in two spatial dimensions, but our construction extends to any spatial dimension and any rotation group (discrete or continuous). We find many possible terms in the equations of motion which are compatible with the existence of an entropy current, but not with the ability to couple the fluid to background gauge fields and vielbein.  more » « less
Award ID(s):
2145544
NSF-PAR ID:
10431406
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2022
Issue:
3
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ( , Journal of Biogeography)
    Abstract Aim

    Area and environmental heterogeneity together explain most patterns of species diversity but disentangling their relative importance has been difficult. Here, we empirically examined this relationship and parsed their relative importance, and that of the heterogeneity—effective area trade‐off, at different spatial scales and in different spatial representations in simulations.

     Location

    Alpine grasslands of 23 mountain ranges of southern and central Europe.

     Taxon

    Vascular plants.

     Methods

    We developed metrics of climatic and edaphic heterogeneity, using principal components analyses and the shoelace algorithm, and added elevation range. We applied commonality analysis to partition the unique and shared explanation of the observed vascular plant species richness among selected metrics. A simulation was developed to separate the relative importance of area and heterogeneity at different extents and representations of spatial nestedness, and the heterogeneity—effective area trade‐off was evaluated by altering spatial discreteness.

     Results

    The explanation of the observed regional richness was shared by area and heterogeneity. The simulation revealed that heterogeneity was consistently more important, but less so among smaller areas. This qualitative pattern was maintained regardless of whether and how nestedness was represented. The heterogeneity–effective area trade‐off occurred in a few simulations of more discrete habitats.

     Main Conclusions

    Scale dependence may account for discrepancies among past empirical studies wherein environmental heterogeneity has usually outweighed area in the explanation of species richness; and it is not affected by nestedness. The potential heterogeneity–effective area trade‐off may be limited to locations where the environmental heterogeneity is quite discrete or if the added environment is beyond the niches of any species in the potential pool. The significant importance of area per se in small territories indicates that microrefugia, even with an unlikely full range of heterogeneity, will suffer local extinctions in the face of climate change.

     
    more » « less
  2. ; ; ( , IMA Journal of Numerical Analysis)
    Abstract In this article, we obtain an optimal best-approximation-type result for fully discrete approximations of the transient Stokes problem. For the time discretization, we use the discontinuous Galerkin method and for the spatial discretization we use standard finite elements for the Stokes problem satisfying the discrete inf-sup condition. The analysis uses the technique of discrete maximal parabolic regularity. The results require only natural assumptions on the data and do not assume any additional smoothness of the solutions. 
    more » « less
  3. ; ; ( , IEEE transactions on automatic control)
    In this article, we revisit the sequential source-coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our results is a new characterization of the lower bound on the minimum total-rate achieved by sequential codes subject to a total (across time) distortion constraint and a computational algorithm that allocates optimally the rate-distortion, for a given distortion level, at each instant of time and any fixed finite-time horizon. The idea behind this characterization facilitates the derivation of analytical , nonasymptotic , and finite-dimensional lower and upper bounds in two control-related scenarios: a) A parallel time-varying Gauss–Markov process with identically distributed spatial components that are quantized and transmitted through a noiseless channel to a minimum mean-squared error decoder; and b) a time-varying quantized linear quadratic Gaussian (LQG) closed-loop control system, with identically distributed spatial components and with a random data-rate allocation. Our nonasymptotic lower bound on the quantized LQG control problem reveals the absolute minimum data-rates for (mean square) stability of our time-varying plant for any fixed finite-time horizon. We supplement our framework with illustrative simulation experiments. 
    more » « less
  4. ; ; ; ( , IEEE Transactions on Computers)
    In this work, we present a novel approach to real-time tracking of full-chip heatmaps for commercial off-the-shelf microprocessors based on machine-learning. The proposed post-silicon approach, named RealMaps, only uses the existing embedded temperature sensors and workload-independent utilization information, which are available in real-time. Moreover, RealMaps does not require any knowledge of the proprietary design details or manufacturing process-specific information of the chip. Consequently, the methods presented in this work can be implemented by either the original chip manufacturer or a third party alike, and is aimed at supplementing, rather than substituting, the temperature data sensed from the existing embedded sensors. The new approach starts with offline acquisition of accurate spatial and temporal heatmaps using an infrared thermal imaging setup while nominal working conditions are maintained on the chip. To build the dynamic thermal model, a temporal-aware long-short-term-memory (LSTM) neutral network is trained with system-level features such as chip frequency, instruction counts, and other high-level performance metrics as inputs. Instead of a pixel-wise heatmap estimation, we perform 2D spatial discrete cosine transformation (DCT) on the heatmaps so that they can be expressed with just a few dominant DCT coefficients. This allows for the model to be built to estimate just the dominant spatial features of the 2D heatmaps, rather than the entire heatmap images, making it significantly more efficient. Experimental results from two commercial chips show that RealMaps can estimate the full-chip heatmaps with 0.9C and 1.2C root-mean-square-error respectively and take only 0.4ms for each inference which suits well for real-time use. Compared to the state of the art pre-silicon approach, RealMaps shows similar accuracy, but with much less computational cost. 
    more » « less
  5. ; ; ( , Journal of the Optical Society of America A)

    We study the radiative transfer of a spatially modulated plane wave incident on a half-space composed of a uniformly scattering and absorbing medium. For spatial frequencies that are large compared to the scattering coefficient, we find that first-order scattering governs the leading behavior of the radiance backscattered by the medium. The first-order scattering approximation reveals a specific curve on the backscattered hemisphere where the radiance is concentrated. Along this curve, the radiance assumes a particularly simple expression that is directly proportional to the phase function. These results are inherent to the radiative transfer equation at large spatial frequency and do not have a strong dependence on any particular optical property. Consequently, these results provide the means by which spatial frequency domain imaging technologies can directly measure the phase function of a sample. Numerical simulations using the discrete ordinate method along with the source integration interpolation method validate these theoretical findings.

     
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email