Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into consider­ably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.

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Deterministic nonperiodic flow

Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a software-defined radio, is defined as an intelligent wireless communication system that is aware of its environment and uses the methodology of understanding-by-building to learn from the environment and adapt to statistical variations in the input stimuli, with two primary objectives in mind: /spl middot/ highly reliable communication whenever and wherever needed; /spl middot/ efficient utilization of the radio spectrum. Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks. 1) Radio-scene analysis. 2) Channel-state estimation and predictive modeling. 3) Transmit-power control and dynamic spectrum management. This work also discusses the emergent behavior of cognitive radio.

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Cognitive radio: brain-empowered wireless communications

/pdf/hydrodynamic-and-hydromagnetic-stability-3nl34xcht5.pdf

Hydrodynamic and Hydromagnetic Stability

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

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Pattern formation outside of equilibrium

Nanocrystals are fundamental to modern science and technology. Mastery over the shape of a nanocrystal enables control of its properties and enhancement of its usefulness for a given application. Our aim is to present a comprehensive review of current research activities that center on the shape-controlled synthesis of metal nanocrystals. We begin with a brief introduction to nucleation and growth within the context of metal nanocrystal synthesis, followed by a discussion of the possible shapes that a metal nanocrystal might take under different conditions. We then focus on a variety of experimental parameters that have been explored to manipulate the nucleation and growth of metal nanocrystals in solution-phase syntheses in an effort to generate specific shapes. We then elaborate on these approaches by selecting examples in which there is already reasonable understanding for the observed shape control or at least the protocols have proven to be reproducible and controllable. Finally, we highlight a number of applications that have been enabled and/or enhanced by the shape-controlled synthesis of metal nanocrystals. We conclude this article with personal perspectives on the directions toward which future research in this field might take.

Shape‐Controlled Synthesis of Metal Nanocrystals: Simple Chemistry Meets Complex Physics?

On The Instability Of Jets

VIII. On the pressure developed in a liquid during the collapse of a spherical cavity

LIX. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side

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On the Capillary Phenomena of Jets

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Lord Rayleigh

Papers

On The Instability Of Jets

VIII. On the pressure developed in a liquid during the collapse of a spherical cavity

LIX. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side

On the Capillary Phenomena of Jets

On Waves Propagated along the Plane Surface of an Elastic Solid