5,396 research outputs found
Continuous-time Algorithms and Analog Integrated Circuits for Solving Partial Differential Equations
Analog computing (AC) was the predominant form of computing up to the end of World War II. The invention of digital computers (DCs) followed by developments in transistors and thereafter integrated circuits (IC), has led to exponential growth in DCs over the last few decades, making ACs a largely forgotten concept. However, as described by the impending slow-down of Mooreâs law, the performance of DCs is no longer improving exponentially, as DCs are approaching clock speed, power dissipation, and transistor density limits. This research explores the possibility of employing AC concepts, albeit using modern IC technologies at radio frequency (RF) bandwidths, to obtain additional performance from existing IC platforms. Combining analog circuits with modern digital processors to perform arithmetic operations would make the computation potentially faster and more energy-efficient. Two AC techniques are explored for computing the approximate solutions of linear and nonlinear partial differential equations (PDEs), and they were verified by designing ACs for solving Maxwell\u27s and wave equations. The designs were simulated in Cadence Spectre for different boundary conditions. The accuracies of the ACs were compared with finite-deference time-domain (FDTD) reference techniques.
The objective of this dissertation is to design software-defined ACs with complementary digital logic to perform approximate computations at speeds that are several orders of magnitude greater than competing methods. ACs trade accuracy of the computation for reduced power and increased throughput. Recent examples of ACs are accurate but have less than 25 kHz of analog bandwidth (Fcompute) for continuous-time (CT) operations. In this dissertation, a special-purpose AC, which has Fcompute = 30 MHz (an equivalent update rate of 625 MHz) at a power consumption of 200 mW, is presented. The proposed AC employes 180 nm CMOS technology and evaluates the approximate CT solution of the 1-D wave equation in space and time. The AC is 100x, 26x, 2.8x faster when compared to the MATLAB- and C-based FDTD solvers running on a computer, and systolic digital implementation of FDTD on a Xilinx RF-SoC ZCU1275 at 900 mW (x15 improvement in power-normalized performance compared to RF-SoC), respectively
Scattering of electromagnetic waves by many thin cylinders: theory and computational modeling
Electromagnetic (EM) wave scattering by many parallel infinite cylinders is
studied asymptotically as a tends to 0, where a is the radius of the cylinders.
It is assumed that the centres of the cylinders are distributed so that their
numbers is determined by some positive function N(x). The function N(x) >= 0 is
a given continuous function. An equation for the self-consistent (limiting)
field is derived as a tends to 0. The cylinders are assumed perfectly
conducting. Formula for the effective refraction coefficient of the new medium,
obtained by embedding many thin cylinders into a given region, is derived. The
numerical results presented demonstrate the validity of the proposed approach
and its efficiency for solving the many-body scattering problems, as well as
the possibility to create media with negative refraction coefficients.Comment: 21 pages, 13 figure
On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability
The Particle-In-Cell (PIC) method is widely used in relativistic particle
beam and laser plasma modeling. However, the PIC method exhibits numerical
instabilities that can render unphysical simulation results or even destroy the
simulation. For electromagnetic relativistic beam and plasma modeling, the most
relevant numerical instabilities are the finite grid instability and the
numerical Cherenkov instability. We review the numerical dispersion relation of
the electromagnetic PIC algorithm to analyze the origin of these instabilities.
We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm,
and then specialize to the Yee FDTD scheme. In particular, we account for the
manner in which the PIC algorithm updates and samples the fields and
distribution function. Temporal and spatial phase factors from solving
Maxwell's equations on the Yee grid with the leapfrog scheme are also
explicitly accounted for. Numerical solutions to the electrostatic-like modes
in the 1D dispersion relation for a cold drifting plasma are obtained for
parameters of interest. In the succeeding analysis, we investigate how the
finite grid instability arises from the interaction of the numerical 1D modes
admitted in the system and their aliases. The most significant interaction is
due critically to the correct represenation of the operators in the dispersion
relation. We obtain a simple analytic expression for the peak growth rate due
to this interaction.Comment: 25 pages, 6 figure
Optimal Control Theory for Continuous Variable Quantum Gates
We apply the methodology of optimal control theory to the problem of
implementing quantum gates in continuous variable systems with quadratic
Hamiltonians. We demonstrate that it is possible to define a fidelity measure
for continuous variable (CV) gate optimization that is devoid of traps, such
that the search for optimal control fields using local algorithms will not be
hindered. The optimal control of several quantum computing gates, as well as
that of algorithms composed of these primitives, is investigated using several
typical physical models and compared for discrete and continuous quantum
systems. Numerical simulations indicate that the optimization of generic CV
quantum gates is inherently more expensive than that of generic discrete
variable quantum gates, and that the exact-time controllability of CV systems
plays an important role in determining the maximum achievable gate fidelity.
The resulting optimal control fields typically display more complicated Fourier
spectra that suggest a richer variety of possible control mechanisms. Moreover,
the ability to control interactions between qunits is important for delimiting
the total control fluence. The comparative ability of current experimental
protocols to implement such time-dependent controls may help determine which
physical incarnations of CV quantum information processing will be the easiest
to implement with optimal fidelity.Comment: 39 pages, 11 figure
Inverse electromagnetic scattering models for sea ice
Journal ArticleInverse scattering algorithms for reconstructing the physical properties of sea ice from scattered electromagnetic field data are presented. The development of these algorithms has advanced the theory of remote sensing, particularly in the microwave region, and has the potential to form the basis for a new generation of techniques for recovering sea ice properties, such as ice thickness, a parameter of geophysical and climatological importance. Moreover, the analysis underlying the algorithms has led to significant advances in the mathematical theory of inverse problems
Communication system for a tooth-mounted RF sensor used for continuous monitoring of nutrient intake
In this Thesis, the communication system of a wearable device that monitors the userâs diet is studied. Based in a novel RF metamaterial-based mouth sensor, different decisions have to be made concerning the systemâs technologies, such as the power source options for the device, the wireless technology used for communications and the method to obtain data from the sensor. These issues, along with other safety rules and regulations, are reviewed, as the first stage of development of the Food-Intake Monitoring projectOutgoin
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