356 research outputs found
Synchronization of Nonlinear Circuits in Dynamic Electrical Networks with General Topologies
Sufficient conditions are derived for global asymptotic synchronization in a
system of identical nonlinear electrical circuits coupled through linear
time-invariant (LTI) electrical networks. In particular, the conditions we
derive apply to settings where: i) the nonlinear circuits are composed of a
parallel combination of passive LTI circuit elements and a nonlinear
voltage-dependent current source with finite gain; and ii) a collection of
these circuits are coupled through either uniform or homogeneous LTI electrical
networks. Uniform electrical networks have identical per-unit-length
impedances. Homogeneous electrical networks are characterized by having the
same effective impedance between any two terminals with the others open
circuited. Synchronization in these networks is guaranteed by ensuring the
stability of an equivalent coordinate-transformed differential system that
emphasizes signal differences. The applicability of the synchronization
conditions to this broad class of networks follows from leveraging recent
results on structural and spectral properties of Kron reduction---a
model-reduction procedure that isolates the interactions of the nonlinear
circuits in the network. The validity of the analytical results is demonstrated
with simulations in networks of coupled Chua's circuits
Ultrasensitive bioluminescent determinations of adenosine triphosphate (ATP) for investigating the energetics of host-grown microbes
Stability and optimal concentrations of reagents were studied in bioluminescence assay of ATP levels. Luciferase enzyme was prepared and purified using Sephadex G-100. Interdependencies between enzyme and luciferin concentrations in presence of optimal Mg are illustrated. Optimal ionic strength was confirmed to be 0.05 M for the four buffers tested. Adapted features of the R- and H-systems are summarized, as well as the percentages of ATP pools released from representative microbes by heat and chloroform
Energetics of the host-dependent Mycobacterium Lepraemurium during transition to a capacity for extracellular growth
The ATP measurements were refined to a point where the growth potential of microscopic samples of host-dependent microbes can be measured, even before an increase in microbial numbers has occurred. This tool differs from other biochemical indicators of physiologic states in its sensitivity and in the fact that it can be exploited with unwashed host-dependent and host-grown organisms
Linear Approximations to AC Power Flow in Rectangular Coordinates
This paper explores solutions to linearized powerflow equations with
bus-voltage phasors represented in rectangular coordinates. The key idea is to
solve for complex-valued perturbations around a nominal voltage profile from a
set of linear equations that are obtained by neglecting quadratic terms in the
original nonlinear power-flow equations. We prove that for lossless networks,
the voltage profile where the real part of the perturbation is suppressed
satisfies active-power balance in the original nonlinear system of equations.
This result motivates the development of approximate solutions that improve
over conventional DC power-flow approximations, since the model includes ZIP
loads. For distribution networks that only contain ZIP loads in addition to a
slack bus, we recover a linear relationship between the approximate voltage
profile and the constant-current component of the loads and the nodal active
and reactive-power injections
Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators
This paper examines the dynamics of power-electronic inverters in islanded
microgrids that are controlled to emulate the dynamics of Van der Pol
oscillators. The general strategy of controlling inverters to emulate the
behavior of nonlinear oscillators presents a compelling time-domain alternative
to ubiquitous droop control methods which presume the existence of a
quasi-stationary sinusoidal steady state and operate on phasor quantities. We
present two main results in this work. First, by leveraging the method of
periodic averaging, we demonstrate that droop laws are intrinsically embedded
within a slower time scale in the nonlinear dynamics of Van der Pol
oscillators. Second, we establish the global convergence of amplitude and phase
dynamics in a resistive network interconnecting inverters controlled as Van der
Pol oscillators. Furthermore, under a set of non-restrictive decoupling
approximations, we derive sufficient conditions for local exponential stability
of desirable equilibria of the linearized amplitude and phase dynamics
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