Drift, Stabilization and Destabilization of Patlak-Keller-Seegel Systems Due to a Short-Wave External Signal

2020 ◽  
pp. 36-48
Author(s):  
Andrey B. Morgulis ◽  
Konstantin I. Ilin
Keyword(s):  
Large Scale ◽  
Short Wave ◽  
Travelling Wave ◽  
Small Scale ◽  
External Signal ◽  
Environmental Fluctuations ◽  
The Stability ◽  
Homogeneous Environment

In this article, we explore a community of two species placed on the inhomogeneous environment. We assume interspecific taxis as well as responding to the environmental fluctuations by tactic movement. We study the effect of the small-scale environmental fluctuations on the large-scale dynamics of the community following the line of Kapitza's theory of the upside-down pendulum. It turns out that, the only conductor of the effect of the fluctuations on the large-scale patterns is some drift of species. When the fluctuation takes the form of a travelling wave, there exist the quasi-equilibria, which are equilibria on average, roughly speaking. Examining the stability of the quasi-equilibria shows that, compared to the case of the homogeneous environment, increasing the magnitude of the fluctuations can destabilize the quasi-equilibria as well as stabilize them. It depends only on the speed at which the fluctuation wave prop-agates which of these effects occurs. Anyway, the effect is exponential in the amplitude of the wave.

scholarly journals Indirect Taxis on a Fluctuating Environment

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2052
Author(s):  
Andrey Morgulis ◽  
Konstantin Ilin
Keyword(s):  
Side Effects ◽  
Pattern Formation ◽  
Large Scale ◽  
Food Resource ◽  
Small Scale ◽  
Fluctuating Environment ◽  
Environmental Fluctuations ◽  
Sea Currents ◽  
Homogeneous Environment

In this article, we study a Patlak–Keller–Siegel (PKS) model of a community of two species placed in the inhomogeneous environment. We employ PKS law for modeling tactic movement due to interspecific taxis and in response to the environmental fluctuations. These fluctuations can arise for natural reasons, e.g., the terrain relief, the sea currents and the food resource distribution, and there are artificial ones. The main result in the article elucidates the effect of the small-scale environmental fluctuations on the large-scale pattern formation in PKS systems. This issue remains uncharted, although numerous studies have addressed the pattern formation while assuming an homogeneous environment. Meanwhile, exploring the role of the fluctuating environment is substantial in many respects, for instance, for predicting the side effects of human activity or for designing the control of biological systems. As well, it is necessary for understanding the roles played in the dynamics of trophic communities by the natural environmental inhomogeneities—those mentioned above, for example. We examined the small-scale environmental inhomogeneities in the spirit of Kapitza’s theory of the upside-down pendulum, but we used the homogenization instead of classical averaging. This approach is novel for the dynamics of PKS systems (though used commonly for other areas). Employing it has unveiled a novel mechanism of exerting the effect from the fluctuating environment on the pattern formation by the drift of species arising upon the homogenization of the fluctuations.

scholarly journals Contact patch memory of tyres leading to lateral vibrations of four-wheeled vehicles

2013 ◽  
Vol 371 (1993) ◽  
pp. 20120427 ◽  
Author(s):  
Dénes Takács ◽  
Gábor Stépán
Keyword(s):  
Large Scale ◽  
Multiple Scales ◽  
Travelling Wave ◽  
Small Scale ◽  
Global Dynamics ◽  
Contact Patch ◽  
Lateral Vibrations ◽  
Wide Range ◽  
The Stability ◽  
Wheeled Vehicles

It has been shown recently that the shimmy motion of towed wheels can be predicted in a wide range of parameters by means of the so-called memory effect of tyres. This delay effect is related to the existence of a travelling-wave-like motion of the tyre points in contact with the ground relative to the wheel. This study shows that the dynamics within the small-scale contact patch can have an essential effect on the global dynamics of a four-wheeled automobile on a large scale. The stability charts identify narrow parameter regions of increased fuel consumption and tyre noise with the help of the delay models that are effective tools in dynamical problems through multiple scales.

scholarly journals Rock Mass Characterization by UAV and Close-Range Photogrammetry: A Multiscale Approach Applied along the Vallone dell’Elva Road (Italy)

Geosciences ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 436
Author(s):  
Maria Migliazza ◽  
Maria Teresa Carriero ◽  
Andrea Lingua ◽  
Emanuele Pontoglio ◽  
Claudio Scavia
Keyword(s):  
Rock Mass ◽  
Large Scale ◽  
Small Scale ◽  
Stability Conditions ◽  
Multiscale Approach ◽  
Rock Mass Characterization ◽  
Geometrical Data ◽  
Close Range ◽  
The Stability ◽  
Kinematic Mechanisms

Geostructural rock mass surveys and the collection of data related to discontinues provide the basis for the characterization of rock masses and the study of their stability conditions. This paper describes a multiscale approach that was carried out using both non-contact techniques and traditional support techniques to survey certain geometrical features of discontinuities, such as their orientation, spacing, and useful persistence. This information is useful in identifying the possible kinematics and stability conditions. These techniques are extremely useful in the case study of the Elva valley road (Northern Italy), in which instability phenomena are spread across 9 km in an overhanging rocky mass. A multiscale approach was applied, obtaining digital surface models (DSMs) at three different scales: large-scale DSM of the entire road, a medium-scale DSM to assess portions of the slope, and a small-scale DSM to assess single discontinuities. The georeferenced point cloud and consequent DSMs of the slopes were obtained using an unmanned aerial vehicle (UAV) and terrestrial photogrammetric technique, allowing topographic and rapid traditional geostructural surveys. This technique allowed us to take measurements along the entire road, obtaining geometrical data for the discontinuities that are statistically representative of the rock mass and useful in defining the possible kinematic mechanisms and volumes of potentially detachable blocks. The main purpose of this study was to analyse how the geostructural features of a rock mass can affect the stability slope conditions at different scales in order to identify road sectors susceptible to different potential failure mechanisms using only kinematic analysis.

Terrain-Forced Flows

2000 ◽  
Author(s):  
C. David Whiteman
Keyword(s):  
Large Scale ◽  
Air Flow ◽  
Windward Side ◽  
Leeward Side ◽  
Small Scale ◽  
Mountainous Terrain ◽  
Jet Streams ◽  
Thermally Driven ◽  
Degree Of Stability ◽  
The Stability

Winds associated with mountainous terrain are generally of two types. Terrain-forced flows are produced when large-scale winds are modified or channeled by the underlying complex terrain. Diurnal mountain winds are produced by temperature contrasts that form within the mountains or between the mountains and the surrounding plains and are therefore also called thermally driven circulations. Terrain-forced flows and diurnal mountain winds are nearly always combined to some extent. Both can occur in conjunction with small-scale winds, such as thunderstorm inflows and outflows, or with large-scale winds that are not influenced by the underlying mountainous terrain. Terrain forcing can cause an air flow approaching a mountain barrier to be carried over or around the barrier, to be forced through gaps in the barrier, or to be blocked by the barrier. Three factors determine the behavior of an approaching flow in response to a mountain barrier: •the stability of the air approaching the mountains, •the speed of the air flow approaching the mountains, and •the topographic characteristics of the underlying terrain. Unstable or neutrally stable air (section 4.3) is easily carried over a mountain barrier. The behavior of stable air approaching a mountain barrier depends on the degree of stability, the speed of the approaching flow, and the terrain characteristics. The more stable the air, the more resistant it is to lifting and the greater the likelihood that it will flow around, be forced through gaps in the barrier, or be blocked by the barrier. A layer of stable air can split, with air above the dividing streamline height flowing over the mountain barrier and air below the dividing streamline height splitting upwind of the mountains, flowing around the barrier (figure 10.1), and reconverging on the leeward side (section 10.3.2). A very stable approaching flow may be blocked on the windward side of the barrier (section 10.5.1). Moderate to strong cross-barrier winds are necessary to produce terrain-forced flows, which therefore occur most frequently in areas of cyclogenesis (section 5.1) or where low pressure systems (figure 1.3) or jet streams (section 5.2.1.3) are commonly found. Whereas unstable and neutral flows are easily lifted over a mountain barrier, even by moderate winds, strong cross-barrier winds are needed to carry stable air over a mountain barrier.

Stability of a Compressible Laminar Wall-Jet With Heat Transfer

1996 ◽  
Vol 118 (4) ◽  
pp. 824-828 ◽  
Author(s):  
O. Likhachev ◽  
A. Tumin
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Wall Jet ◽  
Boundary Layer Equations ◽  
Incompressible Boundary ◽  
Flow Approximation ◽  
Ambient Gas ◽  
The Stability

The flow of a plane, laminar, subsonic perfect gas wall jet with heat transfer through the wall was investigated theoretically. For the case under consideration the entire surface was maintained at a constant temperature which differed from the temperature of the ambient gas. The velocity and temperature distribution across the flow were calculated for a variety of temperature differences between the ambient gas and the surface. The boundary layer equations representing these flows were solved by using the Illingworth-Stewartson transformation, thus extending the classical Glauert’s solution to a thermally non-uniform flow. The effects of heat transfer on the linear stability characteristics of the wall jet were assessed by making the local parallel flow approximation. Two kinds of unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. The influence of cooling or heating on the stability of the flow was expected in view of the experience accumulated in incompressible boundary layers, i.e. heating destabilizes and cooling stabilizes the flows. Cooling of the wall affects the small scale disturbances more profoundly, contrary to the results obtained for the large scale disturbances.

The growth of meteorological disturbances

1949 ◽  
Vol 45 (1) ◽  
pp. 92-98 ◽  
Author(s):  
H. Bondi
Keyword(s):  
Heat Conduction ◽  
Temperature Gradient ◽  
Lower Limit ◽  
Time Scale ◽  
Large Scale ◽  
Ideal Gas ◽  
Small Scale ◽  
Sharp Distinction ◽  
The Subject ◽  
The Stability

1. Introduction. A considerable amount of attention has been paid to the problem of determining the conditions which decide whether a liquid heated from below is stable or unstable. The motion consequent upon the disturbance of an unstable ideal gas does not, however, seem to have been treated so far, and this problem forms the subject of the present paper. Heat conduction and viscosity are at first neglected, and we are therefore dealing with the small motions of a gas slightly disturbed from a position of equilibrium under the influence of gravity. The condition for the stability of such a gas is well known, namely, the temperature gradient must be less than the adiabatic gradient. Furthermore, it is known that there is a sharp distinction between slow large-scale (meteorological) and rapidly varying small-scale (acoustical) phenomena. The present paper confirms these points and derives the time scale of meteorological phenomena. Heat conduction and viscosity are then shown to set a lower limit to the dimensions of such disturbances, while the effect of the earth's rotation is shown to be negligible.

scholarly journals LARGE VERIFICATION TESTS ON ROCK SLOPE STABILITY

1988 ◽  
Vol 1 (21) ◽  
pp. 157
Author(s):  
J.W. Van der Meer ◽  
K.W. Pilarczyk
Keyword(s):  
Large Scale ◽  
Scale Effects ◽  
Rock Slope Stability ◽  
Small Scale ◽  
Rock Slopes ◽  
Ripple Formation ◽  
Scale Test ◽  
Gravel Beaches ◽  
The Stability ◽  
Large Scale Tests

A number of large scale tests on stability of rock slopes and gravel beaches is described and compared with small scale test results. The following topics are treated: the stability of a rock armour layer, the profile formation of a berm breakwater, the profile formation of gravel beaches, including ripple formation, and reflection and overtopping on rock slopes. The general conclusion is that scale effects could not be found.

scholarly journals Thunderstorms Do Not Get Butterflies

2016 ◽  
Vol 97 (2) ◽  
pp. 237-243 ◽  
Author(s):  
Dale R. Durran ◽  
Jonathan A. Weyn
Keyword(s):  
Large Scale ◽  
Squall Line ◽  
Small Scale ◽  
Lead Times ◽  
Initial State ◽  
Weather Forecasts ◽  
Kinetic Energy Spectrum ◽  
Initial Errors ◽  
Squall Lines ◽  
Homogeneous Environment

Abstract One important limitation on the accuracy of weather forecasts is imposed by unavoidable errors in the specification of the atmosphere’s initial state. Much theoretical concern has been focused on the limits to predictability imposed by small-scale errors, potentially even those on the scale of a butterfly. Very modest errors at much larger scales may nevertheless pose a more important practical limitation. We demonstrate the importance of large-scale uncertainty by analyzing ensembles of idealized squall-line simulations. Our results imply that minimizing initial errors on scales around 100 km is more likely to extend the accuracy of forecasts at lead times longer than 3–4 h than efforts to minimize initial errors on much smaller scales. These simulations also demonstrate that squall lines, triggered in a horizontally homogeneous environment with no initial background circulations, can generate a background mesoscale kinetic energy spectrum roughly similar to that observed in the atmosphere.

CFD Study of Generation Process and Stability of a Fire Whirl in Large-Scale Fires

2019 ◽  
Author(s):  
Koyu Satoh ◽  
Domingos Viegas ◽  
Claudia Pinto ◽  
Ran Tu
Keyword(s):  
Forest Fires ◽  
Large Scale ◽  
Small Scale ◽  
Channel Height ◽  
Generation Process ◽  
Strong Wind ◽  
Cfd Simulations ◽  
Swirling Flame ◽  
Fire Whirl ◽  
The Stability

Abstract Large-scale urban and forest fires, especially earthquake-induced fires may produce huge fire whirls and cause serious damage, due to the involved tornado-like strong wind, together with radiation and swirling flame. If fire whirls are generated, the danger to firefighters increases extremely. Many small-scale experiments and CFD simulations on fire whirls have already been conducted and also our previous numerical studies examined the generation of a large fire whirl in an oil tank. However, details of large-scale fire whirls have not been clarified yet. In this study, developing the previous works, additional CFD simulations are conducted to examine the generation process and particularly the stability of fire whirls. Three schemes to generate fire whirls are employed, using the 15 × 15 PMMA fuel array in windy conditions and n-heptane burning in a steel pan placed centrally on the floor in a tall channel with staggered four corner gaps, also using a channel with a single corner gap. The numerical results showed that the relationship between the fire area and the wind blowing area is important on the fire whirl generation in the PMMA scheme and n-heptane fire burning scheme in a channel. In addition to the channel gap size to produce a maximum fire whirl, the effects of channel height and horizontal channel area upon the fire whirl are examined. The wall temperatures of the channel are important to keep the swirling motion stably, particularly the wall temperature at about 300°C can stabilize the fire whirl in a channel. Also multiple small fires placed surrounding the central swirling fire can increase the stability of the fire whirl, although too strong multiple fires may destroy the stability. These phenomena may be related to the real fire whirl generation in the natural environment.

scholarly journals Cirrus clouds triggered by radiation, a multiscale phenomenon

2010 ◽  
Vol 10 (11) ◽  
pp. 5179-5190 ◽  
Author(s):  
F. Fusina ◽  
P. Spichtinger
Keyword(s):  
Large Scale ◽  
Ice Nucleation ◽  
Cirrus Clouds ◽  
Small Scale ◽  
Radiative Cooling ◽  
Cirrus Cloud ◽  
Microphysics Scheme ◽  
Weakly Stable ◽  
The Stability ◽  
Convective Cells

Abstract. In this study, the influence of radiative cooling and small eddies on cirrus formation is investigated. For this purpose the non-hydrostatic, anelastic model EULAG is used with a recently developed and validated ice microphysics scheme (Spichtinger and Gierens, 2009a). Additionally, we implemented a fast radiative transfer code (Fu et al., 1998). Using idealized profiles with high ice supersaturations up to 144% and weakly stable stratifications with Brunt-Vaisala frequencies down to 0.0018 s−1 within a supersaturated layer, the influence of radiation on the formation of cirrus clouds is remarkable. Due to the radiative cooling at the top of the ice supersaturated layer with cooling rates down to −3.5 K/d, the stability inside the ice supersaturated layer decreases with time. During destabilization, small eddies induced by Gaussian temperature fluctuations start to grow and trigger first nucleation. These first nucleation events then induce the growth of convective cells due to the radiative destabilization. The effects of increasing the local relative humidity by cooling due to radiation and adiabatic lifting lead to the formation of a cirrus cloud with IWC up to 33 mg/m3 and mean optical depths up to 0.36. In a more stable environment, radiative cooling is not strong enough to destabilize the supersaturated layer within 8 h; no nucleation occurs in this case. Overall triggering of cirrus clouds via radiation works only if the supersaturated layer is destabilized by radiative cooling such that small eddies can grow in amplitude and finally initialize ice nucleation. Both processes on different scales, small-scale eddies and large-scale radiative cooling are necessary.

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