Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

Asset Price Instability and Policy Responses: The Legacy of Liberalisation

The debate about the dynamics and potential policy responses to asset inflation has intensified in recent years. Some analysts, notably Borio and Lowe, have called for 'subtle' changes to existing monetary targeting frameworks to try to deal with the problems of asset inflation and have attempted to developed indicators of financial vulnerability to aid this process. In contrast, this paper argues that the uncertainties involved in understanding financial market developments and their potential impact on the real economy are likely to remain too high to embolden policy makers. The political and institutional risks associated with policy errors are also significant. The fundamental premise that a liberalised financial system is based on 'efficient' market allocation cannot be overlooked. The corollary is that any serious attempt to stabilize financial market outcomes must involve at least a partial reversal of deregulation.

Contraction of the human diaphragm during rapid postural adjustments

1. The response of the diaphragm to the postural perturbation produced by rapid flexion of the shoulder to a visual stimulus was evaluated in standing subjects. Gastric, oesophageal and transdiaphragmatic pressures were measured together with intramuscular and oesophageal recordings of electromyographic activity (EMG) in the diaphragm. To assess the mechanics of contraction of the diaphragm, dynamic changes in the length of the diaphragm were measured with ultrasonography. 2. With rapid flexion of the shoulder in response to a visual stimulus, EMG-activity in the costal and crural diaphragm occurred about 20 ms prior to the onset of deltoid EMG. This anticipatory contraction occurred irrespective of the phase of respiration in which arm movement began. The onset of diaphragm EMG-coincided with that of transversus abdominis. 3. Gastric and transdiaphragmatic pressures increased in association with the rapid arm flexion by 13.8 +/- 1.9 (mean +/- S.E.M.) and 13.5 +/- 1.8 cmH(2)O, respectively. The increases occurred 49 +/- 4 ms after the onset of diaphragm EMG, but preceded the onset of movement of the limb by 63 +/- 7 ms. 4. Ultrasonographic measurements revealed that the costal diaphragm shortened and then lengthened progressively during the increase in transdiaphragmatic pressure. 5. This study provides definitive evidence that the human diaphragm is involved in the control of postural stability during sudden voluntary movement of the limbs.

Delayed postural contraction of transversus abdominis in low back pain associated with movement of the lower limb

The temporal parameters of the response of the trunk muscles associated with movement of the lower limb were investigated in people with and without low back pain (LBP). The weight shift component of the task was completed voluntarily prior to a stimulus to move to allow investigation of the movement component of the response. In the control subjects the onset of electromyographic (EMG) activity of all trunk muscles preceded that of the muscle responsible for limb movement, thus contributing to the feed forward postural response. The EMG onset of transversus abdominis was delayed in the LBP subjects with movement in each direction, while the EMG onsets of rectus abdominis, erector spinae, and oblique abdominal muscles were delayed with specific movement directions. This result provides evidence of a change in the postural control of the trunk in people with LBP.

Microsatellite instability and loss of heterozygosity at DNA mismatch repair gene loci occurs during hepatic carcinogenesis

DNA mismatch repair is an important mechanism involved in maintaining the fidelity of genomic DNA. Defective DNA mismatch repair is implicated in a variety of gastrointestinal and other turners; however, its role in hepatocellular carcinoma (HCC) has not been assessed. Formalin-fixed, paraffin-embedded archival pathology tissues from 46 primary liver tumors were studied by microdissection and microsatellite analysis of extracted DNA to assess the degree of microsatellite instability, a marker of defective mismatch repair, and to determine the extent and timing of allelic loss of two DNA mismatch repair genes, human Mut S homologue-2 (hMSH2) and human Mut L homologue-1 (hMLH1), and the tumor suppressor genes adenomatous polyposis coli gene (APC), p53, and DPC4. Microsatellite instability was detected in 16 of the tumors (34.8%). Loss of heterozygosity at microsatellites linked to the DNA mismatch repair genes, hMSH2 and/or hMLH1, was found in 9 cases (19.6%), usually in association with microsatellite instability. Importantly, the pattern of allelic loss was uniform in 8 of these 9 tumors, suggesting that clonal loss had occurred. Moreover, loss at these loci also occurred in nonmalignant tissue adjacent to 4 of these tumors, where it was associated with marked allelic heterogeneity. There was relatively infrequent loss of APC, p53, or DPC4 loci that appeared unrelated to loss of hMSH2 or hMLH1 gene loci. Loss of heterozygosity at hMSH2 and/or hMLH1 gene loci, and the associated microsatellite instability in premalignant hepatic tissues suggests a possible causal role in hepatic carcinogenesis in a subset of hepatomas.

Theory of modulational instability in Bragg gratings with quadratic nonlinearity

Modulational instability in optical Bragg gratings with a quadratic nonlinearity is studied. The electric field in such structures consists of forward and backward propagating components at the fundamental frequency and its second harmonic. Analytic continuous wave (CW) solutions are obtained, and the intricate complexity of their stability, due to the large number of equations and number of free parameters, is revealed. The stability boundaries are rich in structures and often cannot be described by a simple relationship. In most cases, the CW solutions are unstable. However, stable regions are found in the nonlinear Schrodinger equation limit, and also when the grating strength for the second harmonic is stronger than that of the first harmonic. Stable CW solutions usually require a low intensity. The analysis is confirmed by directly simulating the governing equations. The stable regions found have possible applications in second-harmonic generation and dark solitons, while the unstable regions maybe useful in the generation of ultrafast pulse trains at relatively low intensities. [S1063-651X(99)03005-6].

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

Activation of the human diaphragm during a repetitive postural task

1. The co-ordination between respiratory and postural functions of the diaphragm was investigated during repetitive upper Limb movement. It was hypothesised that diaphragm activity would occur either tonically or phasically in association with the forces from each movement and that this activity would combine with phasic respiratory activity. 2. Movements of the upper limb and ribcage were measured while standing subjects performed repetitive upper limb movements 'as fast as possible'. Electromyographic (EMG) recordings of the costal diaphragm were made using intramuscular electrodes in four subjects. Surface electrodes were placed over the deltoid and erector spinae muscles. 3. In contrast to standing at rest, diaphragm activity was present throughout expiration at 78 +/- 17% (mean +/- S.D.) of its peak inspiratory magnitude during repeated upper limb movement. 4. Bursts of deltoid and erector spinae EMG activity occurred at the Limb movement frequency (similar to 2.9 Hz). Although the majority of diaphragm EMG power was at the respiratory frequency (similar to 0.4 Hz), a peak was also present at the movement frequency. This finding was corroborated by averaged EMG activity triggered from upper limb movement. In addition, diaphragm EMG activity was coherent with ribcage motion at the respiratory frequency and with upper limb movement at the movement frequency. 5. The diaphragm response was similar when movement was performed while sitting. In addition, when subjects moved with increasing frequency the peak upper limb acceleration correlated with diaphragm EMG amplitude. These findings support the argument that diaphragm contraction is related to trunk control. 6. The results indicate that activity of human phrenic motoneurones is organised such that it contributes to both posture and respiration during a task which repetitively challenges trunk posture.

Chromosomal fragile site FRA16D and DNA instability in cancer

It has been proposed that common aphidicolin-inducible fragile sites, in general, predispose to specific chromosomal breakage associated with deletion, amplification, and/or translocation in certain forms of cancer. Although this appears to be the case for the fragile site FRA3B and may be the case for FRA7G, it is not Set clear whether this association is a general property of this class of fragile site. The major aim of the present study was to determine whether the FRA16D chromosomal fragile site locus has a role to play in predisposing DNA sequences within and adjacent to the fragile site to DNA instability (such as deletion or translocation), which could lead to or be associated with neoplasia. We report the localization of FRA16D within a contig of cloned DNA and demonstrate that this fragile site coincides with a region of homozygous deletion in a gastric adenocarcinoma cell line and is bracketed by translocation breakpoints in multiple myeloma, as reported previously (Chesi, M., et al., Blood, 91: 4457-4463, 1998), Therefore, given similar findings at the FRA3B and FRA7G fragile sites, it is likely that common aphidicolin-inducible fragile sites exhibit the general property of localized DNA instability in cancer cells.

Changes in intra-abdominal pressure during postural and respiratory activation of the human diaphragm

In humans, when the stability of the trunk is challenged in a controlled manner by repetitive movement of a limb, activity of the diaphragm becomes tonic but is also modulated at the frequency of limb movement. In addition, the tonic activity is modulated by respiration. This study investigated the mechanical output of these components of diaphragm activity. Recordings were made of costal diaphragm, abdominal, and erector spinae muscle electromyographic activity; intra-abdominal, intrathoracic, and transdiaphragmatic pressures; and motion of the rib cage, abdomen, and arm. During limb movement the diaphragm and transversus abdominis were tonically active with added phasic modulation at the frequencies of both respiration and limb movement. Activity of the other trunk muscles was not modulated by respiration. Intra-abdominal pressure was increased during the period of limb movement in proportion to the reactive forces from the movement. These results show that coactivation of the diaphragm and abdominal muscles causes a sustained increase in intra-abdominal pressure, whereas inspiration and expiration are controlled by opposing activity of the diaphragm and abdominal muscles to vary the shape of the pressurized abdominal cavity.

Perturbed upper limb movements cause short-latency postural responses in trunk muscles

Addition of a load to a moving upper limb produces a perturbation of the trunk due to transmission of mechanical forces. This experiment investigated the postural response of the trunk muscles in relation to unexpected limb loading. Subjects performed rapid, bilateral shoulder flexion in response to a stimulus. In one third of trials, an unexpected load was added bilaterally to the upper limbs in the first third of the movement. Trunk muscle electromyography, intra-abdominal pressure and upper limb and trunk motion were measured. A short-latency response of the erector spinae and transversus abdominis muscles occurred similar to 50 ms after the onset of the limb perturbation that resulted from addition of the load early in the movement and was coincident with the onset of the observed perturbation at the trunk. The results provide evidence of initiation of a complex postural response of the trunk muscles that is consistent with mediation by afferent input from a site distant to the lumbar spine, which may include afferents of the upper limb.

Postural activity of the diaphragm is reduced in humans when respiratory demand increases

1. Respiratory activity of the diaphragm and other respiratory muscles is normally co-ordinated with their other functions, such as for postural control of the trunk when the limbs move. The integration may occur by summation of two inputs at the respiratory motoneurons. The present study investigated whether postural activity of the diaphragm changed when respiratory drive increased with hypercapnoea. 2. Electromyographic (EMG) recordings of the diaphragm and other trunk muscles were made with intramuscular electrodes in 13 healthy volunteers. Under control conditions and while breathing through increased dead-space,subjects made rapid repetitive arm movements to disturb the stability of the spine for four periods each lasting 10 s, separated by 50 s. 3. End-tidal CO2, and ventilation increased for the first 60-120 s of the trial then reached a plateau. During rapid arm movement at the start of dead-space breathing, diaphragm EMG became tonic with superimposed modulation at the frequencies of respiration and arm movement. However, when the arm was moved after 60 s of hypercapnoea, the tonic diaphragm EMG during expiration and the phasic activity with arm movement were reduced or absent. Similar changes occurred for the expiratory muscle transversus abdominis, but not for the erector spinae. The mean amplitude of intra-abdominal pressure and the phasic changes with arm movement were reduced after 60 s of hypercapnoea. 4. The present data suggest that increased central respiratory drive may attenuate the postural commands reaching motoneurons. This attenuation can affect the key inspiratory and expiratory muscles and is likely to be co-ordinated at a pre-motoneuronal site.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.