Time-Dependent Dynamics of a Planar Galaxy Model

Time-dependent models of collisionless stellar systems with harmonic potentials allowing for an essentially exact analytic description have recently been described. These include oscillating spheres and spheroids. This paper extends the analysis to time-dependent elliptic discs. Although restricted to two space dimensions, the systems are richer in that their parameters form a 10-dimensional phase space (in contrast to six for the earlier models). Apart from total energy and angular momentum, two additional conserved quantities emerge naturally. These can be chosen as the areas of extremal sections of the ellipsoidal region of phase space occupied by the system (their product gives the conserved volume). The present paper describes the construction of these models. An application to a tidal encounter is given which allows one to go beyond the impulse approximation and demonstrates the effects of rotation of the perturbed system on energy and angular-momentum transfer. The angular-momentum transfer is shown to scale inversely as the cube of the encounter velocity for an initial configuration of the perturbed galaxy with zero quadrupole moment.

Homonuclear NOE in spatially periodic spin systems

The nuclear Overhauser effect equations are solved analytically for a homonuclear group of spins whose sites are periodically arranged, including the special cases where the spins lie at the vertices of a regular polygon and on a one-dimensional lattice. t is shown that, for long correlation times, the equations governing magnetization transfer resemble a diffusion equation. Furthermore the deviation from exact diffusion is quantitatively related to the molecular tumbling correlation time. Equations are derived for the range of magnetization travel subsequent to the perturbation of a single spin in a lattice for both the case of strictly dipolar relaxation and the more general situation where additional T1 mechanisms may be active. The theory given places no restrictions on the delay (or mixing) times, and it includes all the spins in the system. Simulations are presented to confirm the theory.

Specification of Real-Time Systems

Inspite of numerous research advancements made in recent years in the area of formal techniques, specification of real-time systems is still proving to be a very challenging and difficult problem. In this context, this paper critically examines state-of-the-art specification techniques for real-time systems and analyzes the emerging trends.

High-Rate Space-Time Coded Large MIMO Systems: Low-Complexity Detection and Performance

Large MIMO systems with tens of antennas in each communication terminal using full-rate non-orthogonal space-time block codes (STBC) from Cyclic Division Algebras (CDA) can achieve the benefits of both transmit diversity as well as high spectral efficiencies. Maximum-likelihood (ML) or near-ML decoding of these large-sized STBCs at low complexities, however, has been a challenge. In this paper, we establish that near-ML decoding of these large STBCs is possible at practically affordable low complexities. We show that the likelihood ascent search (LAS) detector, reported earlier by us for V-BLAST, is able to achieve near-ML uncoded BER performance in decoding a 32x32 STBC from CDA, which employs 32 transmit antennas and sends 32(2) = 1024 complex data symbols in 32 time slots in one STBC matrix (i.e., 32 data symbols sent per channel use). In terms of coded BER, with a 16x16 STBC, rate-3/4 turbo code and 4-QAM (i.e., 24 bps/Hz), the LAS detector performs close to within just about 4 dB from the theoretical MIMO capacity. Our results further show that, with LAS detection, information lossless (ILL) STBCs perform almost as good as full-diversity ILL (FD-ILL) STBCs. Such low-complexity detectors can potentially enable implementation of high spectral efficiency large MIMO systems that could be considered in wireless standards.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Conflict-Tolerant Real-Time Specifications in Metric Temporal Logic

A framework based on the notion of "conflict-tolerance" was proposed in as a compositional methodology for developing and reasoning about systems that comprise multiple independent controllers. A central notion in this framework is that of a "conflict-tolerant" specification for a controller. In this work we propose a way of defining conflict-tolerant real-time specifications in Metric Interval Temporal Logic (MITL). We call our logic CT-MITL for Conflict-Tolerant MITL. We then give a clock optimal "delay-then-extend" construction for building a timed transition system for monitoring past-MITL formulas. We show how this monitoring transition system can be used to solve the associated verification and synthesis problems for CT-MITL.

Continuous-time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximated using a parametric positive semi-definite function. Unlike earlier approaches, a continuous-time weight update law is derived from the HJB equation. The stability of the system is analysed during the evolution of weights using Lyapunov theory. The effectiveness of the scheme is demonstrated through simulation examples.

Continous Time Sigma-Delta Modulator Employing a Novel Comparator Architecture

A novel comparator architecture is proposed for speed operation in low voltage environment. Performance comparison with a conventional regenerative comparator shows a speed-up of 41%. The proposed comparator is embedded in a continuous time sigma-delta ADC so as to reduce the quantizer delay and hence minimizes the excess loop delay problem. A performance enhancement of 1dB in the dynamic range of the ADC is achieved with this new comparator. We have implemented this ADC in a standard single-poly 8-Metal 0.13 mum UMC process. The entire system operates at 1.2 V supply providing a dynamic range of 32 dB consuming 720 muW of power and occupies an area of 0.1 mm2.

Average variation L2-stability criteria for time-varying feedback systems-A unified approach

The problem of developing L2-stability criteria for feedback systems with a single time-varying gain, which impose average variation constraints on the gain is treated. A unified approach is presented which facilitates the development of such average variation criteria for both linear and nonlinear systems. The stability criteria derived here are shown to be more general than the existing results.

Class of linear time-varying discrete systems

A class of linear time-varying discrete systems is considered, and closed-form solutions are obtained in different cases. Some comments on stability are also included.

Real-time density matrix renormalization group dynamics of spin and charge transport in push-pull polyenes and related systems

In this paper we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes [D-(CH)(x)-A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D-(CH)(x)-A system, and time-dependent density matrix renormalization group technique for time propagating the wave packet obtained by injecting a hole at a terminal site, in the ground state of the system. Our studies reveal that the end groups do not affect spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these push-pull systems with donor-acceptor substituted polymethine imine (PMI), D-(CHN)(x)-A, systems in which besides electron affinities, the nature of p(z) orbitals in conjugation also alternate from site to site. We note that spin and charge dynamics in the PMIs are very different from that observed in the case of push-pull polyenes, and within the time scale of our studies, transport of spin and charge leads to the formation of a ``quasi-static'' state.