skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: A toy model for the relativistic Vlasov-Maxwell system
The global-in-time existence of classical solutions to the relativistic Vlasov-Maxwell (RVM) system in three space dimensions remains elusive after nearly four decades of mathematical research. In this note, a simplified "toy model" is presented and studied. This toy model retains one crucial aspect of the RVM system: the phase-space evolution of the distribution function is governed by a transport equation whose forcing term satisfies a wave equation with finite speed of propagation.  more » « less
Award ID(s):
2107938 1911145
PAR ID:
10332115
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Kinetic and Related Models
Volume:
15
Issue:
3
ISSN:
1937-5093
Page Range / eLocation ID:
341
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. (, Risks)
    We study a toy model of linear-quadratic mean field game with delay. We “lift" the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward Hamilton-Jacobi-Bellman equation. We identify the corresponding master equation. A solution to this master equation is computed, and we show that it provides an approximation to a Nash equilibrium of the finite player game. 
    more » « less
  2. ; (, New Journal of Physics)
    Abstract We investigate the dynamics of two quantum mechanical oscillator system–bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar quantum electrodynamics (QED). The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular operational probes of the decoherence for initial scalar field system superposition states. 
    more » « less
  3. ; ; ; ; ; ; (, Sensors)
    In this paper, we evaluate the uniqueness of a hypothetical iris recognition system that relies upon a nonlinear mapping of iris data into a space of Gaussian codewords with independent components. Given the new data representation, we develop and apply a sphere packing bound for Gaussian codewords and a bound similar to Daugman’s to characterize the maximum iris population as a function of the relative entropy between Gaussian codewords of distinct iris classes. As a potential theoretical approach leading toward the realization of the hypothetical mapping, we work with the auto-regressive model fitted into iris data, after some data manipulation and preprocessing. The distance between a pair of codewords is measured in terms of the relative entropy (log-likelihood ratio statistic is an alternative) between distributions of codewords, which is also interpreted as a measure of iris quality. The new approach to iris uniqueness is illustrated using two toy examples involving two small datasets of iris images. For both datasets, the maximum sustainable population is presented as a function of image quality expressed in terms of relative entropy. Although the auto-regressive model may not be the best model for iris data, it lays the theoretical framework for the development of a high-performance iris recognition system utilizing a nonlinear mapping from the space of iris data to the space of Gaussian codewords with independent components. 
    more » « less
  4. (, Mathematische Nachrichten)
    Abstract Three control problems for the system of two coupled differential equations governing the dynamics of an energy harvesting model are studied. The system consists of the equation of an Euler–Bernoulli beam model and the equation representing the Kirchhoff's electric circuit law. Both equations contain coupling terms representing the inverse and direct piezoelectric effects. The system is reformulated as a single evolution equation in the state space of 3‐component functions. The control is introduced as a separable forcing term on the right‐hand side of the operator equation. The first control problem deals with an explicit construction of that steers an initial state to zero on a time interval [0,T]. The second control problem deals with the construction of such that the voltage output is equal to some given function (with being given as well). The third control problem deals with an explicit construction of both the force profile, , and the control, , which generate the desired voltage output . Interpolation theory in the Hardy space of analytic functions is used in the solution of the second and third problems. 
    more » « less
  5. (, Journal of High Energy Physics)
    A<sc>bstract</sc> The Gepner model (2)4describes the sigma model of the Fermat quartic K3 surface. Moving through the nearby moduli space using conformal perturbation theory, we investigate how the conformal weights of its fields change at first and second order and find approximate minima. This serves as a toy model for a mechanism that could produce new chiral fields and possibly new nearby rational CFTs. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email