Type Of Instability Research Articles

Spatial pattern formation in activator-inhibitor models with nonlocal dispersal

<p style='text-indent:20px;'>The stability of a constant steady state in a general reaction-diffusion activator-inhibitor model with nonlocal dispersal of the activator or inhibitor is considered. It is shown that Turing type instability and associated spatial patterns can be induced by fast nonlocal inhibitor dispersal and slow activator diffusion, and slow nonlocal activator dispersal also causes instability but may not produce stable spatial patterns. The existence of nonconstant positive steady states is shown through bifurcation theory. This suggests a new mechanism for spatial pattern formation, which has different instability parameter regime compared to Turing mechanism. The theoretical results are applied to pattern formation problems in nonlocal Klausmeier-Gray-Scott water-plant model and Holling-Tanner predator-prey model.

Different responses of the Rayleigh–Taylor type and resistive drift wave instabilities to the velocity shear

The effects of velocity shear on the unstable modes driven by the effective gravity (Rayleigh–Taylor and interchange) and resistive drift wave instabilities for inhomogeneous equilibrium fluid/plasma density are analyzed for the localized eigenmode problems. It is shown that the effect of the velocity shear drastically depends on the type of instability. Whereas the velocity shear can significantly suppress both Rayleigh–Taylor and interchange instabilities, it has only a weak impact on the growth rate of the resistive drift wave. This is directly related to the physical nature of these instabilities. For the Rayleigh–Taylor and interchange instabilities, the shear flow tilts the eddies of the stream functions, while for the resistive drift wave instability the shear flow simply shifts the eddies in the radial direction with no tilting. However, for a large velocity shear, the eigenmode solutions for resistive drift waves cease to exist.

A Measurement System to Monitor Postural Behavior: Strategy Assessment and Classification Rating

Postural instability is a symptom of disorders like ear diseases, high blood pressure, diabetes, psychiatric disorders, and neurodegenerative diseases like Parkinson and one of the main causes of falls. A continuous monitoring of the patient’s postural stability while performing the daily activities would be of strategic interest for the doctors to gain continuous information on the user pathology or its progression. This article focuses on the experimental assessment of a wearable inertial device aimed at the continuous monitoring of the user’s postural sway, which exploits a novel postural sway classification algorithm providing a classification index. Two performance keys have been proposed: 1) to assess the postural sway monitoring strategy and 2) to rate the reliability of the classification outcome. Experiments reported in this article have been performed involving “healthy” users miming typical instability dynamics under the supervision of the neurologists. In the case of study addressed through this article, a full classification success has been obtained with an overall reliability of about 70%.

О ГЛАДКОЙ ИНТЕРПОЛЯЦИИ ТРИАНГУЛИРОВАННОЙ ПОВЕРХНОСТИ

A method and algorithm for rebuilding a surface triangulation in three-dimensional space defined by an STL file is proposed. An initial surface in 3D space (STL file) is represented as a polyhedron composed of triangular faces. The method is based on the analytical representation of the surface as a piecewise polynomial function. This function is built on a polyhedral surface composed of triangles and satisfies the following requirements: 1) within one face, the function is an algebraic polynomial of the third degree; 2) the function is continuous on the entire surface and preserves the continuity of the first partial derivatives; 3) the surface determined by the function passes through the vertices of the initial triangulated surface. The restructuring of computational meshes is required in cases of distortion of the shape of cells when solving problems of mathematical physics using mesh methods (finite-difference, FEM, etc.). Cell distortion can be due to various reasons. These can be large distortions of moving Lagrangian meshes in the calculations in the current configuration, with instability of the hourglass type, with distortion of the faces of the interface between interacting gaseous, liquid and elastoplastic bodies. The rebuilding of the mesh reduces to solving the problem of constructing a smooth surface passing through the nodes of an existing triangulated surface or part of it. Later the nodes of the new mesh are placed on the constructed smooth surface with existing requirements for the size and shape of the cells. The construction of a smooth piecewise polynomial surface is based on the ideas of spline approximation and reduces to the building of a cubic polynomial on each triangular face, taking into account the smooth conjugation of polynomial pieces of the surface constructed on adjacent faces. The proposed method for rebuilding surface triangulation can be useful for calculating the motion of deformable bodies when solving problems of the dynamics of continuous media on immovable Euler grids.

Turing type instability in a diffusion model with mass transport on the boundary

<p style="text-indent:20px;">Some reaction-diffusion models describing the cell polarity are proposed, where the system has two independent variables standing for the concentration of proteins in the membrane and the cytosol respectively. In this article we deal with such a polarity model consisting of one equation on a unit sphere and the other one in the ball inside the sphere. The two equations are coupled through a nonlinear boundary condition and the total mass is conserved. We investigate the linearized stability of a constant steady state and provide conditions under which a Turing type instability takes place, namely, the constant state is stable against spatially uniform perturbations on the sphere for all choices of diffusion rates, while unstable against nonuniform perturbations on the sphere as the diffusion coefficient of the equation on the sphere becomes small relative to the one in the ball.

Experimental observation of coexisting electromagnetic fluctuations correlating with the inter-ELM pedestal evolution on EAST

Correlations between the edge fluctuations and the pedestal evolution during the relatively large edge localized mode (ELM) cycles at high pedestal normalized electron collisionality (νe,ped* &amp;gt; 1) on the EAST tokamak are investigated. Not only the edge electrostatic coherent mode (ECM, ∼50 kHz) and the low frequency magnetic coherent mode (MCM, ∼32 kHz) but also a high frequency electromagnetic mode (HFM, &amp;gt;150 kHz) are observed to be coexisting between ELMs. After the ELM crash, the pedestal electron temperature recovered faster than the pedestal electron density. It is found that the saturation of the ECM coincides more with the saturation of the pedestal electron density, while the saturation of the HFM and MCM coincides more with the saturation of the pedestal electron temperature. In addition, the characteristics of the electromagnetic fluctuations (the HFM and MCM) are studied in detail: the HFM propagates in the electron diamagnetic drift direction in the laboratory frame with an average poloidal wave number of k¯θHFM≈0.17 cm−1, while the MCM propagates in the ion diamagnetic drift direction in the laboratory frame with k¯θMCM ≈ 0.12 cm−1 and the toroidal mode number of n = 1. Furthermore, both the HFM and MCM have inward average radial wave numbers of k¯RHFM≈0.13 cm−1 and k¯RMCM≈4.64 cm−1. The bispectral analysis shows that the HFM and MCM have strong nonlinear interactions. The HFM is clearly observed on both low and high field side Mirnov coils, which might suggest a feature beyond a ballooning type instability, e.g., the kinetic ballooning mode. These studies may contribute to a better understanding of the pedestal evolution.

Experimental characterization of a quasi-coherent turbulent structure in the edge plasma in Wendelstein 7-X

A quasi-coherent mode (QCM) near the plasma edge is characterized experimentally by measuring the density fluctuation via a poloidal correlation reflectometer (PCR) in Wendelstein 7-X. This QCM frequency descends from 25 kHz near the separatrix to 10 kHz as the cutoff position penetrates toward the core. A similar mode structure is also observed in the spectra of electron cyclotron emission edge channels and Mirnov coil signals, which shows a clear correlation with respect to the PCR measurement. The mode evaluation yields a range for the poloidal mode number of , and for the normalized mode scale , which suggest a drift type instability. The QCM structure appears in the standard and narrow-mirror configurations (both with the rotational transform in the boundary), but is absent in the high- configuration (boundary ). The impact of plasma parameters on the QCM is discussed. It is observed that the QCM frequency and amplitude can be affected by the edge magnetic topology and plasma parameters. The shifts upward during the negative and non-stellarator-symmetric control coil current scans, which may be attributed to the effect of the shear, Er, and ne in the plasma edge region.

Meltblown technology for production of polymeric microfibers/nanofibers: A review

This work summarizes the current state of knowledge in the area of meltblown technology for production of polymeric nonwovens with specific attention to utilized polymers, die design, production of nanofibers, the effect of process variables (such as the throughput rate, melt rheology, melt temperature, die temperature, air temperature/velocity/pressure, die-to-collector distance, and speed) with relation to nonwoven characteristics as well as to typical flow instabilities such as whipping, die drool, fiber breakup, melt spraying, flies, generation of small isolated spherical particles, shots, jam, and generation of nonuniform fiber diameters.

Molten Metal Jets Formation in the Cathode Spot of a Vacuum Arc

We have theoretically studied the molten metal jets formation during an operation of vacuum arc discharge for a wide range of crater sizes for near-threshold electric currents. At the initial stage of crater formation, a liquid-metal rim forms on the cathode surface under the action of the cathode spot plasma pressure. This process has been numerically simulated in the framework of the 2-D axisymmetric heat and mass transfer problem in the approximation of viscous incompressible liquid. At the next stage, jets form due to the loss of axial symmetry of the rim (the problem becomes essentially 3-D). The development of the Rayleigh–Plateau (RP) and Rayleigh–Taylor instabilities of the rim are analyzed in terms of dispersion relations for surface waves. It is shown that maximum increments correspond to the capillary instability of the RP type. The calculated time of rim formation and that of its breakup into jets have been demonstrated to be comparable. The analysis of rim perturbation spectrum has allowed to estimate probable number of liquid-metal jets.

The free surface effect on a chemotaxis–diffusion–convection coupling system

Suspension of an oxytactic bacteria (e.g. the species Bacillus subtilis) placed in a container with its upper surface open to the atmosphere results in the formation of complex bioconvection patterns. The bacteria consume the oxygen diluted in the water, thereby causing the decrease of oxygen concentration everywhere except on the free surface. Through the free surface, which is in direct contact with the air, oxygen diffuses into the water. Slightly denser than water, the oxytactic bacteria are able to swim towards the higher concentration of oxygen (i.e. upwards) and they concentrate in a thin layer below the free surface. This causes the change of the suspension density and Rayleigh–Taylor type instabilities to occur. The chemotaxis phenomenon has been successfully modeled within continuum mechanics approach under certain simplifications. The set of (non-linearly) coupled equations describing the process involves the Boussinesq approximation of the Navier–Stokes equations governing the fluid motion and two convection–diffusion type equations governing the bacteria and oxygen concentrations. One of the simplifications that might significantly influence numerical simulations is the boundary condition for fluid equation on the free surface. This condition ensures that the vertical component of the velocity is zero, thus keeping the position of free surface fixed. This assumption significantly simplifies numerical procedure since the non-linearly coupled system can then be solved on stationary grid. However, allowing the motion of the free surface and completing the system with appropriate boundary conditions on contact line (liquid–solid–gas interface), a more realistic model is derived and new insights on nonlinear dynamics of the chemotaxis phenomenon are obtained. Our aims in this paper are to upgrade the currently available model into a more realistic one in both two and three dimensions, to propose a numerical procedure to deal with the new system (now posed on time-dependent domain) and, finally, to show the difference between this new model and the previous simplified one.

Frictional effect on stability of discontinuity interface in tangential velocity of a shallow-water flow

We examine a frictional effect on the linear stability of an interface of discontinuity in tangential velocity. The fluid is moving with uniform velocity U in a region but is at rest in the other, and the bottom surface is assumed to exert drag force, quadratic in velocity, on the thin fluid layer. In the absence of the drag, the instability of the Kelvin-Helmholtz type is suppressed for U>8c, with c being the propagating speed of the gravity wave. We find by asymptotic analyses for both small and large values of the drag strength that the drag, regardless of its strength, makes the flow unstable for the whole range of the Froude number U/c.

Stability analysis of predator–prey models involving cross-diffusion

Abstract In this paper we have considered a three dimensional system of partial differential equations to model the dynamical interactions of two predators competing for a single prey. The model is developed by introducing cross diffusion in such a way as to take into account the migratory strategy adopted by the predators, who take advantage of the defense switching behavior of the prey. Equilibria of the model are determined and a local stability analysis is discussed. The main result presented here is that for certain range of values of the cross diffusion parameters, the system has a continuum of equilibria and a zip-type bifurcation occurs and this is not sustainable due to the emergence of Turing type instability.

An efficient approach for post-buckling analysis of sandwich structures with elastic-plastic material behavior

This paper aims to propose an efficient and accurate framework for the post-buckling analysis of sandwich structures with elastic-plastic material behaviors. Correspondingly, efforts are made in two aspects, i.e., the model and the nonlinear solver. A new one-dimensional sandwich model is firstly established, in which the skins are described by Euler–Bernoulli beam theory, while the core layer is approximated by high-order functions. The Ramberg–Osgood elastic-plastic material behavior is considered for the core and the linear elastic for the skins. Green–Lagrange strains are used for accurately describing large deformations in both skins and core layer. The resulting nonlinear equations are then solved by an efficient and robust path-following technique, i.e., the Asymptotic Numerical Method (ANM), in which the bifurcation indicator is introduced to precisely detect bifurcation points and the corresponding instability patterns. Several typical instability phenomena (global buckling, local-global-coupling instability and shear crimping) are investigated and numerical results demonstrate that the proposed approach is able to accurately characterize the post-buckling behaviors of sandwich structures with few computational cost.

The effects of surface tension on modulational instability in full-dispersion water-wave models

We study the modulational instability of a shallow water model, with and without surface tension, which generalizes the Whitham equation to include bi-directional propagation. Without surface tension, the small amplitude periodic traveling waves are modulationally unstable if their wave number is greater than a critical wave number predicting a Benjamin–Feir type instability and the result qualitatively agrees with the shallow water model in Hur and Pandey (2016). With surface tension, the result qualitatively agrees with the physical problem except for the large surface tension limit which is accurately predicted by the shallow water model in Hur and Pandey (2016). We also compare the results with the Whitham and full-dispersion Camassa–Holm equations. We conclude that the shallow water model in Hur and Pandey (2016) is a better model than the shallow water model presented here when the effects of surface tension on modulational instability is considered.

Influence of wear on hot banding migration of sealing ring using FEM

Hot banding is a typical thermoelastic instability phenomenon that occurs on the sealing surface of the sealing ring in a transmission. The presence of hot banding on sealing contact surfaces causes local wear. The wear of a sealing ring results in the loss of supply pressure and ultimately causes transmission failure. Local wear and hot banding migration also affect each other. This paper has discussed the influence of the wear of the sealing interface on hot banding migration using the general finite element method. A wear simulation procedure, based on Archard's wear law, was used to calculate the wear of the sealing ring, and the thermoelastic effects were also included in the simulation model. An iterative cyclic updating method was performed using the general finite element analysis software. The results of the simulation showed how wear influenced the migration of the hot banding. The worn sealing surfaces lead to more complex migration states of the hot banding, including division and combination of the hot banding. The proposed simulation method and the procedure that was used are suitable for trend analysis of seal design.

10 kHz simultaneous PIV/PLIF study of the diffusion flame response to periodic acoustic forcing.

Response of a laminar diffusion dimethyl-ether flame forced by an acoustic field is provided. A forcing frequency of 100 Hz, which is chosen based on the typical thermo-acoustic instability frequency in a practical combustor, is applied to the flame at a Reynolds number of 250. The development of the forced vortical structures present in this flame has been investigated utilizing a burst mode laser with a repetition rate of 10 kHz. Flame/vortex interaction is visualized by planar laser-induced fluorescence (PLIF) of formaldehyde, which is used to identify the early-stage fuel decomposition in the flame. The flame structure is also correlated with the velocity field, which is obtained utilizing particle imaging velocimetry (PIV). The resulting phase-resolved and time-averaged velocity and vortex images indicate that the amplitude of excitation has pronounced effects on the flame via modifying the local heat release.

Investigating The Role of TMPRSS1 In Mouse Inner Ear Structure And Function

Hearing loss is one of the common birth defects in humans. Defects in the type II transmembrane serine proteases (TMPRSS) have been reported to affect organic structures of the inner ears, and thus, hearing function in mice, including loss of TMPRSS1 or any of at least 4 other TMPRSS members. Here, we used the human TMPRSS1 transgenic (hTMPRSS1‐Tg) mice on a mouse TMPRSS1‐null background to investigate the rescue function of exogenously‐expressed TMPRSS1 in the development of hearing and inner ears. The expression of hTMPRSS1 was detected in the organ of Corti and stria vascularis in the inner ear. Phenotype analysis using auditory brainstem evoked response (ABR) test showed that while the TMPRSS1‐null mice exhibited profound hearing loss as literally reported, the deafness of hTMPRSS1‐Tg mice were alleviated partially with 20 dB improvement. The H&amp;E stain showed that the anomaly of the tectorial membrane in hTMPRSS1‐Tg mice was less serious than the TMPRSS1‐null mice. Although the hearing threshold had positive correlation with the area of the tectorial membrane, no significant difference was calculated. To further analyze the components in tectorial membrane, we used immunofluorescence to quantify molecules mainly expressed on tectorial membrane: α‐tectorin, β‐tectorin, type IX collagen, type II collagen of wild‐type and TMPRSS1‐null mice. The result showed that while α‐ and β‐tectorin and type IX collagen were less homogenously expressed in TMPRSS1‐null mice. Similar results were noted in electronic microscopy. Since α‐ and β‐tectorin form the underlying striated‐sheet matrix in the tectorial membrane, our results suggested that suboptimal connection of α‐tectorin with β‐tectorin could lead to the instability of type IX collagen, causing the deformity of tectorial membrane and consequently deafness in TMPRSS1‐null mice. TMPRSS1 indeed plays an important role in hearing. Transgenic/knockout mice established in our lab was a great tool for studying the add‐back effect of TMPRSS1 for hearing improvement, and may help develop therapies on certain patients with congenital hearing loss in the future.Support or Funding InformationThis study is supported by MOST (107‐2319‐B‐002‐001 and 104‐2314‐B‐002‐159)This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Descriptions of Entropy with Fractal Dynamics and Their Applications to the Flow Pressure of Centrifugal Compressor.

In this study, some important intrinsic dynamics have been captured after analyzing the relationships between the dynamic pressure at an outlet of centrifugal compressor and fractal characteristics, which is one of powerful descriptions in entropy to measure the disorder or complexity in the nonlinear dynamic system. In particular, the fractal dynamics of dynamic pressure of the flow is studied, as the centrifugal compressor is in surge state, resulting in the dynamic pressure of flow and becoming a serious disorder and complex. First, the dynamic pressure at outlet of a centrifugal compressor with 800 kW is tested and then obtained by controlling the opening of the anti-surge valve at the outlet, and both the stable state and surge are initially tested and analyzed. Subsequently, the fractal dynamics is introduced to study the intrinsic dynamics of dynamic pressure under various working conditions, in order to identify surge, which is one typical flow instability in centrifugal compressor. Following fractal dynamics, the Hurst exponent, autocorrelation functions, and variance in measure theories of entropy are studied to obtain the mono-fractal characteristics of the centrifugal compressor. Further, the multi-fractal spectrums are investigated in some detail, and their physical meanings are consequently explained. At last, the statistical reliability of multi-fractal spectrum by modifying the original data has been studied. The results show that a distinct relationship between the dynamic pressure and fractal characteristics exists, including mono-fractal and multi-fractal, and such fractal dynamics are intrinsic. As the centrifugal compressor is working under normal condition, its autocorrelation function curve demonstrates apparent stochastic characteristics, and its Hurst exponent and variance are lower. However, its autocorrelation function curve demonstrates an apparent heavy tail distribution, and its Hurst exponent and variance are higher, as it is working in an unstable condition, namely, surge. In addition, the results show that the multi-fractal spectrum parameters are closely related to the dynamic pressure. With the state of centrifugal compressor being changed from stable to unstable states, some multi-fractal spectrum parameters Δα, Δf(α), αmax, and f(αmin) become larger, but αmin in the multi-fractal spectrum show the opposite trend, and consistent properties are graphically shown for the randomly shuffled data. As a conclusion, the proposed method, as one measure method for entropy, can be used to feasibly identify the incipient surge of a centrifugal compressor and design its surge controller.

Gyrokinetic investigations on entropy modes in dipole magnetic field confined plasmas with an anisotropic temperature

Entropy modes are typical instabilities particularly seen in dipole field confined plasmas. In this paper, linear gyrokinetic calculations, together with the integral dispersion relation method, are applied to study the electrostatic entropy mode in such plasmas with an anisotropic temperature. The numerical approach is verified for certain typical conditions with previous studies. We then further focus on the anisotropic temperature effect on the entropy mode. Basic characteristics of the entropy mode are obtained with the effect. The results show that the entropy mode has a peak growth rate at kρi ∼ 1, and the mode is shifted from the ion to the electron diamagnetic regimes at small k⊥ρi. This work can be applied for various dipole magnetic field confined plasmas as well as certain other configurations, such as Z-pinch and field reversed configurations.

Investigation of the dynamics in separated turbulent flow

Abstract Dynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation ( Dns ). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number R e τ ranging from 125 to 730 where R e τ is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wall-shear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortex-shedding type instability of the bubble. A low-frequency self-sustained oscillation associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration.