Spectrum Of Instability Research Articles

Dispersive wave in the modulation instability spectrum in the presence of noise

We present the dispersive wave (DW) in the dispersion-shifted fibre (DSF) based on numerical simulations, which causes the symmetry-breaking of the modulation instability (MI) spectrum. It is demonstrated that the DW power is related to both pump power and three-order dispersion (TOD). It is found in particular that different levels of noise also have relations with the generation of a DW, which essentially results from the fact that MI is initiated from noise and there exists power transfer between the MI (soliton) and DW. Furthermore, we study the spectral autocorrelation within the Stokes and anti-Stokes bands in the presence of the DW, which show the property of very weak autocorrelation for a continuous wave (CW) or quasi-CW. The results provide further understanding of the symmetry and correlation of the MI spectrum.

Turbulent plasma transport across the Earth's low‐latitude boundary layer

AbstractThe Kelvin‐Helmholtz instability is a key process for the transport of solar wind plasma into the Earth's magnetosphere when the interplanetary magnetic field (IMF) is northward. Previous kinetic simulations for symmetric layers have demonstrated that the flow vortices compress the magnetopause current layer and induce magnetic reconnection, leading to the rapid streaming of solar wind plasma into the vortices along newly reconnected field lines. Using fully kinetic 3‐D simulations, we demonstrate that the inherent density asymmetry across the boundary layer leads to a spectrum of oblique interchange instabilities along the magnetospheric side of the vortices. These secondary instabilities give rise to turbulence, which transports the solar wind plasma originally stored within the flow vortices deep into the magnetosphere. Simple estimates suggest that this turbulent transport may contribute significantly to the formation of the Earth's low‐latitude boundary layer and the cold‐dense plasma sheet during prolonged periods of northward IMF.

A practical approach to goal-directed echocardiography in the critical care setting.

Urgent cardiac ultrasound examination in the critical care setting is clinically useful. Application of goal-directed echocardiography in this setting is quite distinct from typical exploratory diagnostic comprehensive echocardiography, because the urgent critical care setting mandates a goal-directed approach. Goal-directed echocardiography most frequently aims to rapidly identify and differentiate the cause(s) of hemodynamic instability and/or the cause(s) of acute respiratory failure. Accordingly, this paper highlights 1) indications, 2) an easily memorized differential diagnostic framework for goal-directed echocardiography, 3) clinical questions that must be asked and answered, 4) practical issues to allow optimal image capture, 5) primary echocardiographic views, 6) key issues addressed in each view, and 7) interpretation of findings within the differential diagnostic framework. The most frequent indications for goal-directed echocardiography include 1) the spectrum of hemodynamic instability, shock, and pulseless electrical activity arrest and 2) acute respiratory failure. The differential diagnostic categories for hemodynamic instability can be remembered using the mnemonic ‘SHOCK’ (for Septic, Hypovolemic, Obstructive, Cardiogenic, and (K) combinations/other kinds of shock). RESP-F (for exacerbation of chronic Respiratory disease, pulmonary Embolism, ST changes associated with cardiac or pericardial disease, Pneumonia, and heart Failure) can be used for acute respiratory failure. The goals of goal-directed echocardiography in the unstable patient are: assessing global ventricular systolic function, identifying marked right ventricular and left ventricular enlargement, assessing intravascular volume, and the presence of a pericardial effusion. In an urgent or emergent setting, it is recommended to go directly to the best view, which is frequently the subcostal or apical view. The five views are the subcostal four-chamber view, subcostal inferior vena cava view, parasternal long axis view, parasternal short axis view, and the apical four chamber view. Always interpret goal-directed echocardiographic findings in the context of clinically available hemodynamic information. When goal-directed echocardiography is insufficient or when additional abnormalities are appreciated, order a comprehensive echocardiogram. Goal-directed echocardiography and comprehensive echocardiography are not to be used in conflict with each other.

The instability spectrum of weakly-magnetized SU(2) Reissner–Nordström black holes

It is well known that the U(1) Reissner–Nordström black hole is stable within the framework of the Einstein–Maxwell theory. However, the SU(2) Reissner–Nordström black-hole solution of the coupled Einstein–Yang–Mills equations is known to be unstable. In fact, this magnetically charged black hole is characterized by an infinite set of unstable (growing in time) perturbation modes. In the present paper we study analytically the instability resonance spectrum of weakly-magnetized SU(2) Reissner–Nordström black holes. In particular, we obtain explicit analytical expressions for the infinite set {ωn}n=0n=∞ of imaginary eigenvalues that characterize the instability growth rates of the perturbation modes. We discuss the role played by these unstable eigenvalues as critical exponents in the gravitational collapse of the Yang–Mills field. Finally, it is shown that our analytical formulas for the characteristic black-hole instability spectrum agree with new numerical data that recently appeared in the literature.

Modulation instability in metamaterials with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites

The linearized nonlinear propagation equation and its coefficients, gain spectrum of modulation instability (MI) in metamaterials (MMs) with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites, are analytically deduced by utilizing the linear stability analysis and Drude electromagnetic model. Then variations of gain spectra of MI with the normalized angular frequencies and the optical power densities are calculated in real units. In the negative refractive region, two kinds of gain spectra are discovered. The first (second) one is close to (far from) the zero perturbation frequencies and it corresponds to the lower (higher) normalized angular frequencies. Moreover, the second one has higher cutoff frequency, which is obviously beneficial to generation of high-repetition-rate pulse trains. While in the positive refractive region, only the first kind of gain spectra is found. With increase of the optical power densities, the peak gains and the spectral widths of MI increase before decrease, but they vary the most rapidly (slowly) for the exponential (conventional) saturable nonlinearities. The MI characteristics and their corresponding applications can be adjusted by several methods.

Gain sideband splitting in dispersion oscillating fibers

We analyze the modulation instability spectrum in a varying dispersion optical fiber as a function of the dispersion oscillation amplitude. For large dispersion oscillations, we predict a novel sideband splitting into different sub-sidebands. The emergence of the new sidebands is observed whenever the classical perturbation analysis for parametric resonances predicts vanishing sideband amplitudes. The numerical results are in good quantitative agreement with Floquet or Bloch stability analysis of four-wave mixing in the periodic dispersion fiber. We have also shown that linear gain or loss may have a dramatic influence in reshaping the new sidebands.

A 1.37-Mb 12p11.22–p11.21 deletion coincident with a 367-kb 22q11.2 duplication detected by array comparative genomic hybridization in an adolescent girl with autism and difficulty in self-care of menstruation

ObjectiveTo present an array comparative genomic hybridization (aCGH) characterization of a 12p11.22–p11.21 microdeletion and 22q11.2 microduplication in an adolescent girl with autism, mental retardation, facial dysmorphism, microcephaly, behavior problems, and an apparently balanced reciprocal translocation of t(8;12)(q24.3;p11.2). Materials and methodsA 13-year-old girl was referred to the hospital because of autism, mental retardation, and difficulty in the self-care of her menstruation. Cytogenetic analysis revealed an apparently balanced reciprocal translocation and a karyotype of 46,XX,t(8;12) (q24.3;p11.2)dn. The girl manifested microcephaly, hypertelorism, flat facial profile, prominent forehead, thick scalp hair, upslanting palpebral fissures, broad nasal bridge, bulbous nose, right simian crease, bilateral clinodactyly of the fifth fingers, bilateral pes cavus, learning difficulties, mental retardation, emotional instability, cognitive impairment, behavior problems, jumping-like gaits, and autistic spectrum disorder. aCGH was performed to evaluate genomic imbalance in this patient. ResultsaCGH analysis revealed a 1.37-Mb 12p11.22–p11.21 microdeletion or arr [hg 19] 12p11.22-p11.21 (30,645,008–32,014,774)×1 and a 367-kb 22q11.21 microduplication or arr [hg 19] 22q11.21 (18,657,470–19,024,306)×3. The 1.37-Mb 12p11.22–p11.21 microdeletion encompassed 26 genes including IPO8, CAPRIN2, and DDX11, and the 367-kb 22q11.21 microduplication encompassed 20 genes including USP18, DGCR6, PRODH, and DGCR2. ConclusionAn apparently balanced translocation may be in fact affected by concurrent deletion and duplication in two different chromosomal regions. Our presentation provides information on diagnostic phenotype of 12p11.22–p11.21 microdeletion and 22q11.2 microduplication.

Impact of higher-order dispersion in the modulational instability spectrum of a relaxing coupled saturable media

A theoretical analysis of modulational instability (MI) of optical pulses propagating near the zero dispersion wavelength of a lossless fibre with the effect of delayed saturable nonlinear response is presented. We calculate the exact dispersion relation with the effect of higher dispersion for the harmonic perturbation. We analysed the impact of fourth-order dispersion effects in the MI spectrum. We examine the possibility of MI in both dispersion regimes, regardless of the sign of the group velocity dispersion.

Recurrent anterior shoulder instability: Review of the literature and current concepts.

The purpose of this review article is to discuss the clinical spectrum of recurrent traumatic anterior shoulder instability with the current concepts and controversies at the scientific level. Because of increasing participation of people from any age group of the population in sports activities, health care professionals dealing with the care of trauma patients must have a thorough understanding of the anatomy, patho-physiology, risk factors, and management of anterior shoulder instability. The risk factors for recurrent shoulder dislocation are young age, participation in high demand contact sports activities, presence of Hill-Sachs or osseous Bankart lesion, previous history of ipsilateral traumatic dislocation, ipsilateral rotator cuff or deltoid muscle insufficiency, and underlying ligamentous laxity. Achieving the best result for any particular patient depends on the procedure that allows observation of the joint surfaces, provides the anatomical repair, maintains range of motion, and also can be applied with low rates of complications and recurrence. Although various surgical techniques have been described, a consensus does not exist and thus, orthopedic surgeons should follow and try to improve the current evidence-based treatment modalities for the patients.

DIFFERENCES BETWEEN REAL AND PARTICLE-IN-CELL PLASMAS: EFFECTS OF COARSE-GRAINING

The PIC model relies on two building blocks. The first stems from the capability of computers to handle only up to ~ 1010 particles, while real plasmas contain from 104 to 1020 particles per Debye sphere: a coarse-graining step must be used, whereby of the order of p ~ 1010 real particles are represented by a single computer superparticle. The second is field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e. physical quantities depending on the number p. They all derive from the plasma parameter Λ, which we show to be proportional to 1/p. We explore three examples: the rapid collision- and fluctuation-induced thermalization of plasmas with different temperatures, that scale with the number of superparticles per grid cell and are a factor p ~ 1010 faster than in real plasmas; the high level of electrostatic fluctuations in a thermal plasma, with corrections due to the finite superparticle sizes; and the blurring of the linear spectrum of the filamentation instability, where the fastest growing modes do not dominate the total energy because of a high level of fluctuations. We stress that the enhanced collisions and correlations of PIC plasmas must be kept negligible toward kinetic physics.

The Landscape of Microsatellite Instability in Colorectal and Endometrial Cancer Genomes

Microsatellites-simple tandem repeats present at millions of sites in the human genome-can shorten or lengthen due to a defect in DNA mismatch repair. We present here a comprehensive genome-wide analysis of the prevalence, mutational spectrum, and functional consequences of microsatellite instability (MSI) in cancer genomes. We analyzed MSI in 277 colorectal and endometrial cancer genomes (including 57 microsatellite-unstable ones) using exome and whole-genome sequencing data. Recurrent MSI events in coding sequences showed tumor type specificity, elevated frameshift-to-inframe ratios, and lower transcript levels than wild-type alleles. Moreover, genome-wide analysis revealed differences in the distribution of MSI versus point mutations, including overrepresentation of MSI in euchromatic and intronic regions compared to heterochromatic and intergenic regions, respectively, and depletion of MSI at nucleosome-occupied sequences. Our results provide a panoramic view of MSI in cancer genomes, highlighting their tumor type specificity, impact on gene expression, and the role of chromatin organization.

Modulation instability in nonlinear propagation of pulses in optical fibers

We consider a generalized system consisting of two coupled Schrödinger-type equations which models nonlinear pulse propagation in a linearly birefringent Kerr optical fiber. An analysis of stability of periodic solutions of the system is performed by using a second-order accurate spectral numerical solver. The main novelty in our study is that we do not assume high or weak birefringence in the fiber and thus the model considered incorporates nonlinear terms which were neglected in the stability analysis performed in previous works. In the case of anomalous dispersion, our numerical simulations indicate that a periodic solution develops a type of modulation instability against small disturbances, given that the perturbation frequency remains within certain range (computed analytically by means of a linear analysis) which depends on the model’s parameters and the amplitude of the perturbing signals. We also find that the gain spectrum of modulation instability is altered by the additional nonlinear terms included in the above-mentioned system.

Management of Hip Instability in Trisomy 21

The unstable hip in Trisomy 21 presents with a spectrum of hip instability with different problems at different ages. What links this multiphase problem, in many patients, is the final common pathway of untreated instability, that of a stiff, dislocated, and often-painful hip, leading to significant functional disability. Historically, the results of treating hip instability in Trisomy 21 were variable with a notable frequency of poor results. With an improved understanding of the Trisomy 21 hip in terms of its pathoanatomy and a more contemporary surgical approach to hip reconstruction, much improved results can be expected and indeed have recently been shown. The mainstay of treatment for the habitual dislocation group presenting before 8 years of age is the femoral varus derotation osteotomy. The older group presenting with painful subluxation often show signs of secondary acetabular dysplasia and thus are best treated with redirectional acetabular osteotomy with or without the use of femoral varus derotation osteotomy. The presence of radiographic features of degenerative arthritis in the fixed dislocation group precludes the use of joint-preserving techniques for hip reconstruction, and these patients can achieve excellent results with total joint arthroplasty. The natural history, historical results, assessment, treatment, and management of complications of hip instability in Trisomy 21 are addressed in this paper.

Nonlinear dynamical modelling of chaotic electrostatic ion cyclotron oscillations by jerk equations

Plasma being a nonlinear and complex system, is capable of sustaining a wide spectrum of waves, oscillations and instabilities. These fluctuations interact nonlinearly amongst themselves and also with particles: electrons/ions and thus lead to nonlinear wave-wave or wave-particle interaction. In the presence of coherent waves the particles are accelerated whereas irregular oscillations can give rise to particle heating which is also called stochastic heating. Particle orbits are known to be randomized by the wave fields such that their motion can also become stochastic. For fusion to be sustained one needs a very high temperature plasma for an extended duration. It quite common to deploy external waves like electron cyclotron waves or ion cyclotron waves for plasma heating and current drive. These external waves also work only in certain regimes. Conventional plasma techniques have been able to answer several of the observations of the above processes related to heating transport etc, but nonlinear dynamics as a tool has helped in comprehending the plasma oscillations better. We have for the first time obtained a Third Order nonlinear ordinary differential equation (TONLODE) also known as jerk equation to describe the electrostatic ion cyclotron plasma oscillations in a magnetic field. The interesting feature of this equation is that it does not require an external forcing term to obtain chaotic behaviour.

Observation of two state behavior in the instability spectra of saturable nonlinear media

We investigate the modulational instability (MI) in the saturable nonlinear system (SNL). We identified the unique behavior of MI in the SNL system, which we called as the two state behavior. Unlike the case of Kerr type nonlinearity the so called critical modulational frequency does not monotonously increases, rather behaves in such way, that the increase in power increases the CMF upto the saturation power, and further increase in power decreases the CMF. This behavior is identified to be unusual in the context of MI and thus makes the study of MI interesting.

Traumatic instability of the elbow - anatomy, pathomechanisms and presentation on imaging

Traumatic instability of the elbow is a common problem among patients presenting to emergency departments. As recurrent instability is more common than previously thought and the knowledge of the most frequent underlying causes increases, treatment of elbow instability is becoming increasingly sophisticated. Therefore, it is mandatory for the radiologist to be familiar with the important osseous and soft-tissue stabilisers of the elbow joint and to know the pathomechanisms that lead to a spectrum of joint instability. This article discusses the relevant anatomy in elbow stability with respect to imaging and function, states the mechanisms leading to elbow dislocation and displays the types of traumatic instability of the elbow on radiography, computed tomography, and magnetic resonance imaging. • Expert imaging helps the management of traumatic instability of the elbow • The lateral ulnar collateral ligament is the cornerstone for elbow stability • Soft-tissue disruption is important in posterolateral rotatory instability • Identification of small coronoid process fragments is essential for optimal surgical therapy.

Interplay between relaxation of nonlinear response and coupling coefficient dispersion in the instability spectra of dual core optical fiber

The modulational instability of a dual core optical fiber under the combined effect of coupling coefficient dispersion (CCD) and relaxation of nonlinear response is presented. The effect of wavelength dependence of coupling coefficient is effectively included in the pair of generalized linearly coupled nonlinear Schrödinger equation (CNLSE). In order to account for the finite response time, a time dependent nonlinear response is incorporated in the system of CNLSE using the Debye relaxation model. The results from the linear stability analysis show that in anomalous dispersion regime for any finite relaxation time, the nonlinearity becomes complex and there exist two unstable modes. In the normal dispersion regime, a single unstable band at higher detuning frequency is observed which is identified as the Raman band. In symmetric case the CCD is found to be immaterial, whereas in asymmetric case the CCD is found to be crucial and brings new spectral bands. A critical value of CCD is predicted where the dynamics evolve dramatically in different manners. Thus in this paper, the MI dynamics of a dual core optical fiber is fully explored and the interplay between CCD and relaxation is clearly highlighted.

Modulational instability in a twin-core fiber with the effect of saturable nonlinear response and coupling coefficient dispersion

Modulational instability (MI) in a twin-core optical fiber with the combined effect of saturation of nonlinearity (SNL) and coupling coefficient dispersion (CCD) is presented. The CCD does not dramatically modify the spectrum of the symmetric or antisymmetric continuous wave (CW) case, but the SNL on the other hand behaves in a perceptible manner such that the gain and the unstable region inherently decrease. In the anomalous dispersion region, the gain of the instability spectrum increases (decreases) monotonously with power (coupling coefficient). The effective nonlinearity and the power threshold for the sustained CW solution becomes a function of power for the SNL case. The so-called nonlinear factor behaves in a unique way such that there exist two powers for the same value of nonlinear factor. The interplay between CCD and SNL is emphasized, where any nonzero value of CCD leads to new instability bands and the saturation on the other hand suppresses the gain of the instability band. We identified a pair of power corresponding to the constant value of the nonlinear factor, where the system becomes invariant, such that the number of instability bands, the gain, and the range of the unstable region are all preserved. In the case of the normal dispersion case, the MI is achieved purely by means of the coupling coefficient. In both cases, a critical CCD is predicted, where the system evolves dramatically in a different manner.

Impact of fourth-order dispersion in the spectra of polarization-modulational instability in highly nonlinear fibers

Impact of fourth-order dispersion in the spectra of polarization-modulational instability in highly nonlinear fibers

Measuring single-shot modulation instability and supercontinuum spectra at megahertz rates**This invited article is one of a series published throughout 2011, 2012 and 2013 in Nonlinearity on the topic of Rogue Waves.

Single-shot spectra of modulation instability (MI) and long-pulse supercontinuum (SC) are acquired at megahertz repetition rates (using time-stretch dispersive Fourier transformation) and analysed over a broad wavelength range. We find varied statistical distributions—including heavy-tailed, bimodal, Gaussian-like, and hybrid forms—depending on the input parameters and selected output wavelength. These distributions are investigated with the aid of simulations, which show that that the redshifted energy and peak intensity of the individual events are well correlated for low soliton number. Similar experimental and simulated single-shot spectra are also found, suggesting that input noise conditions can be accurately identified. The library of spectra provides new insights into noise-driven MI and long-pulse SC generation at the single-shot level.