Pattern generation by dissipative parametric instability

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems, ranging from biology to galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the dissipative parametric instability can lead to the formation of stable patterns in one- and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems.

Primary production, financial constraints and economic instability:Zambia since independence.

A systematic analysis is presented of the economic consequences of the abnormally high concentration of Zambia's exports on a commodity whose price is exceptionally unstable. Zambian macro-economic variables in the post-independence years are extensively documented, showing acute instability and decline, particularly after the energy price revolution and the collapse of copper prices. The relevance of stabilization policies designed to correct short-term disequilibrium is questioned. It is, therefore, a pathological case study of externally induced economic instability, complementing other studies in this area which use cross-country analysis of a few selected variables. After a survey of theory and issues pertaining to development, finance and stabilization, the emergence of domestic and foreign financial constraints on the Zambian economy is described. The world copper industry is surveyed and an examination of commodity and world trade prices concludes that copper showed the highest degree of price instability. Specific aspects of Zambia's economy identified for detailed analysis include: its unprofitable mining industry, external payments disequilibrium, a constrained government budget, potentially inflationary monetary growth, and external indebtedness. International comparisons are used extensively, but major copper exporters are subjected to closer scrutiny. An appraisal of policy options concludes the study.

Lateral instability of slender reinforced concrete columns in a fire environment

The research concerns the development and application of an analytical computer program, SAFE-ROC, that models material behaviour and structural behaviour of a slender reinforced concrete column that is part of an overall structure and is subjected to elevated temperatures as a result of exposure to fire. The analysis approach used in SAFE-RCC is non-linear. Computer calculations are used that take account of restraint and continuity, and the interaction of the column with the surrounding structure during the fire. Within a given time step an iterative approach is used to find a deformed shape for the column which results in equilibrium between the forces associated with the external loads and internal stresses and degradation. Non-linear geometric effects are taken into account by updating the geometry of the structure during deformation. The structural response program SAFE-ROC includes a total strain model which takes account of the compatibility of strain due to temperature and loading. The total strain model represents a constitutive law that governs the material behaviour for concrete and steel. The material behaviour models employed for concrete and steel take account of the dimensional changes caused by the temperature differentials and changes in the material mechanical properties with changes in temperature. Non-linear stress-strain laws are used that take account of loading to a strain greater than that corresponding to the peak stress of the concrete stress-strain relation, and model the inelastic deformation associated with unloading of the steel stress-strain relation. The cross section temperatures caused by the fire environment are obtained by a preceding non-linear thermal analysis, a computer program FIRES-T.

Purchasing power parity and structural instability in the US/UK exchange rate

The aim of this study is to determine if nonlinearities have affected purchasing power parity (PPP) since 1885. Also using recent advances in the econometrics of structural change we segment the sample space according to the identified breaks and look at whether the PPP condition holds in each sub-sample and whether this involves linear or non-linear adjustment. Our results suggest that during some sub-periods, PPP holds, although whether it holds or not and whether the adjustment is linear or non-linear, depends primarily on the type of exchange rate regime in operation at any point in time.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Risk and structural instability in US house prices

This paper employs a Component GARCH in Mean model to show that house prices across a number of major US cities between 1987 and 2009 have displayed asset market properties in terms of both risk-return relationships and asymmetric adjustment to shocks. In addition, tests for structural breaks in the mean and variance indicate structural instability across the data range. Multiple breaks are identified across all cities, particularly for the early 1990s and during the post-2007 financial crisis as housing has become an increasingly risky asset. Estimating the models over the individual sub-samples suggests that over the last 20 years the financial sector has increasingly failed to account for the levels of risk associated with real estate markets. This result has possible implications for the way in which financial institutions should be regulated in the future.

Dual-pump Raman amplification with increased flatness using modulation instability

he application of modulation instability-initiated nonlinear broadening of two CW pumps at different wavelengths, in order to achieve superior gain ripple performance in broadband Raman amplifiers, is demonstrated for the first time experimentally. A particular example using Truewave and LEAF fibers is offered, in which the 0.1 dB gain ripple band is extended from 5 nm to 19 nm. Experimental results are in a good agreement with numerical modeling. Guidelines for optimal broadening are discussed.

Dual-pump Raman amplification with increased flatness using modulation instability

The application of modulation instability-initiated nonlinear broadening of two CW pumps at different wavelengths, in order to achieve superior gain ripple performance in broadband Raman amplifiers, is demonstrated for the first time experimentally. A particular example using Truewave and LEAF fibers is offered, in which the 0.1 dB gain ripple band is extended from 5 nm to 19 nm. Experimental results are in a good agreement with numerical modeling. Guidelines for optimal broadening are discussed. © 2005 Optical Society of America.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Power-controlled phase-matching and instability of CW propagation in multicore optical fibers with a central core

We present modulation instability analysis including azimuthal perturbations of steady-state continuous wave (CW) propagation in multicore-fiber configurations with a central core. In systems with a central core, a steady CW evolution regime requires power-controlled phase matching, which offers interesting spatial-division applications. Our results have general applicability and are relevant to a range of physical and engineering systems, including high-power fiber lasers, optical transmission in multicore fiber, and systems of coupled nonlinear waveguides. © 2013 Optical Society of America.

Design of a fiber scheme for nonlinear Raman pump broadening through modulation instability

In this work we explore numerically an experimentally the dependence of the broadened spectra on the choice of fibers and we analyze a series of basic rules to be taken into account when using nonlinear broadening to reduce the gain ripple of broadband Raman amplifiers

Dual-pump Raman amplification with enhanced flatness using modulation instability

In this work, we utilize modulation instability to the broadening of the two CW-pumps of a wideband Raman amplifier. Applying nonlinear fiber process, we demonstrate a feasibility of a certain control over the broadening process, leading to clear improvements in the flatness of the amplifier gain over its operational bandwidth.

The role of pinning and instability in a class of non-equilibrium growth models

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the "perturbative" limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behaviour. Possibilities of controlling this instability by introducing statistically "irrelevant" (in the sense of renormalisation groups) higher ordered nonlinearities have also been discussed.

Modulation instability in high power laser amplifiers

The modulation instability (MI) is one of the main factors responsible for the degradation of beam quality in high-power laser systems. The so-called B-integral restriction is commonly used as the criteria for MI control in passive optics devices. For amplifiers the adiabatic model, assuming locally the Bespalov-Talanov expression for MI growth, is commonly used to estimate the destructive impact of the instability. We present here the exact solution of MI development in amplifiers. We determine the parameters which control the effect of MI in amplifiers and calculate the MI growth rate as a function of those parameters. The safety range of operational parameters is presented. The results of the exact calculations are compared with the adiabatic model, and the range of validity of the latest is determined. We demonstrate that for practical situations the adiabatic approximation noticeably overestimates MI. The additional margin of laser system design is quantified. © 2010 Optical Society of America.