Snap-Through of Shallow Extensible Arches Under Unilateral Displacement Control

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
Raymond H. Plaut
Keyword(s):  
Equilibrium Configuration ◽  
Critical Value ◽  
Unstable Equilibrium ◽  
Vertical Position ◽  
Displacement Control ◽  
Critical Displacement ◽  
Push Down

Critical displacements are determined for snap-through of shallow, extensible, and elastic arches that are pushed downward quasi-statically at any point along the span. The initial arch is circular and unstrained, and the ends of the arch are pinned and immovable. When the vertical position at the push-down location reaches a critical value, the arch jumps into an inverted shape (unless the arch is extremely shallow). The critical displacement is given or approximated by an unstable equilibrium configuration of the unloaded arch, for which an analyical formula is derived.

scholarly journals Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations

1997 ◽  
Vol 43 (143) ◽  
pp. 71-79 ◽  
Author(s):  
G. Hilmar Gudmundsson
Keyword(s):  
Flow Characteristics ◽  
Local Maximum ◽  
Critical Value ◽  
Two Dimensions ◽  
Creeping Flow ◽  
Wave Number ◽  
Vertical Position ◽  
Gravity Driven ◽  
The Mean ◽  
Basal Flow

AbstractThe basal deformation of a gravity-driven linear creeping flow sliding frictionless over slowly varying bed undulations in two dimensions is analysed analytically, using results from second-order perturbation theory. One of the key results is that, close to sinusoidal bedrock undulations, up to two different spatial regions of local extrusion flow may arise. The offset and onset of extrusion flow is controlled primarily by the amplitude-to-wavelength ratio. Above the crest of a sinusoidal bed line, a local maximum of the surface-parallel velocity develops for ε : =ak< 0.138, whereais the amplitude andkis the wave number. Asεincreases from zerо to this critical value, the vertical position of the velocity maximum moves fromkz= 1 tokz≈ 1.98, wherezis the vertical distance above the mean bed line. Within and above the trough of a sinusoid, a region of local minimum of the surface-parallel velocity component develops, which shifts fromkz= 1 towards the bed line asεincreases front zero to 1/2. Below this velocity minimum, and for some distance above the velocity maximum, the surface-parallel velocity increases with depth. This type of extrusion flow will cause a reversal of borehole-inclination profiles close to the bedrock.

Interactions Between Self and Parametrically Excited Motions in Articulated Tubes

1984 ◽  
Vol 51 (2) ◽  
pp. 423-429 ◽  
Author(s):  
A. K. Bajaj
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Parametric Resonance ◽  
Flow Rate ◽  
Critical Value ◽  
Mean Value ◽  
Vertical Position ◽  
Linearized System ◽  
The Mean ◽  
Stable Solutions

The nonlinear dynamics of a two-segment articulated tubes system conveying a fluid is studied when the flow is harmonically perturbed. The mean value of the flow rate is near its critical value when the downward vertical position gets unstable and undergoes Hopf bifurcation into periodic solutions. The harmonic perturbations are assumed to be in parametric resonance with the linearized system. The method of Alternate Problems is used to obtain the small nonlinear subharmonic solutions of the system. It is shown that, in addition to the usual jump response, the system also exhibits stable and unstable isolated solution branches. For some parameter combinations the stable solutions can become unstable and can then bifurcate into aperiodic or amplitude-modulated motions.

The erosion of a distributed two-dimensional vortex in a background straining flow

2001 ◽  
Vol 441 ◽  
pp. 369-398 ◽  
Author(s):  
BERNARD LEGRAS ◽  
DAVID G. DRITSCHEL ◽  
PHILIPPE CAILLOL
Keyword(s):  
Thin Filament ◽  
Equilibrium Configuration ◽  
Critical Value ◽  
Leading Order ◽  
Linear Deformation ◽  
Intermediate Period ◽  
Elliptical Model ◽  
Rapid Elongation ◽  
Shape Deformations

Herein we present a simplified theory for the behaviour of a vortex embedded in a growing external straining flow. Such a flow arises naturally as a vortex moves relative to other vortices. While the strain may generally exhibit a complex time dependence, the salient features of the vortex evolution can be understood in the simpler context, studied here, of a linearly growing strain. Then, all of the typical stages of evolution can be seen, from linear deformation, to the stripping or erosion of low-lying peripheral vorticity, and finally to the breaking or rapid elongation of the vortex into a thin filament.When, as is often the case in practice, the strain growth is slow, the vortex adjusts itself to be in approximate equilibrium with the background flow. Then, the vortex passes through, or near, a sequence of equilibrium states until, at a critical value of the strain, it suddenly breaks. In the intermediate period before breaking, the vortex continuously sheds peripheral vorticity, thereby steepening its edge gradients. This stripping is required to keep the vortex in a near equilibrium configuration.We show that this behaviour can be captured, quantitatively, by a reduced model, the elliptical model, which represents the vortex by a nested set of elliptical vorticity contours, each having a (slightly) different aspect ratio and orientation. Here, we have extended the original elliptical model by allowing for edge vorticity levels to be shed when appropriate (to represent stripping) and by incorporating the flow induced by the vorticity being stripped away. The success of this model proves that the essential characteristics of vortex erosion are captured simply by the leading-order, elliptical shape deformations of vorticity contours.Finally, we discuss the role of viscosity. Then, there is a competition between gradient steepening by stripping and smoothing by viscosity. If the strain grows too slowly, the vortex is dominated by viscous decay, and the edge gradients become very smooth. On the other hand, for sufficiently rapid strain growth (which can still be slow, depending on the viscosity), the vortex edge remains steep until the final breaking.

scholarly journals Basal-flow characteristics of a linear medium sliding frictionless over small bedrock undulations

1997 ◽  
Vol 43 (143) ◽  
pp. 71-79 ◽  
Author(s):  
G. Hilmar Gudmundsson
Keyword(s):  
Flow Characteristics ◽  
Local Maximum ◽  
Critical Value ◽  
Two Dimensions ◽  
Creeping Flow ◽  
Wave Number ◽  
Vertical Position ◽  
Gravity Driven ◽  
The Mean ◽  
Basal Flow

AbstractThe basal deformation of a gravity-driven linear creeping flow sliding frictionless over slowly varying bed undulations in two dimensions is analysed analytically, using results from second-order perturbation theory. One of the key results is that, close to sinusoidal bedrock undulations, up to two different spatial regions of local extrusion flow may arise. The offset and onset of extrusion flow is controlled primarily by the amplitude-to-wavelength ratio. Above the crest of a sinusoidal bed line, a local maximum of the surface-parallel velocity develops for ε : = ak < 0.138, where a is the amplitude and k is the wave number. As ε increases from zerо to this critical value, the vertical position of the velocity maximum moves from kz = 1 to kz ≈ 1.98, where z is the vertical distance above the mean bed line. Within and above the trough of a sinusoid, a region of local minimum of the surface-parallel velocity component develops, which shifts from kz = 1 towards the bed line as ε increases front zero to 1/2. Below this velocity minimum, and for some distance above the velocity maximum, the surface-parallel velocity increases with depth. This type of extrusion flow will cause a reversal of borehole-inclination profiles close to the bedrock.

Magnetoelastic Buckling of a Thin Plate

1968 ◽  
Vol 35 (1) ◽  
pp. 53-58 ◽  
Author(s):  
F. C. Moon ◽  
Yih-Hsing Pao
Keyword(s):  
Magnetic Field ◽  
Axial Load ◽  
Uniform Magnetic Field ◽  
Field Experiments ◽  
Equilibrium Configuration ◽  
Critical Value ◽  
Transverse Magnetic ◽  
Field Equations ◽  
Magnetostatic Field ◽  
Characteristic Values

The instability of a column under axial load is well known. A similar phenomenon is discussed in this paper for a beam-plate in a transverse magnetic field. Experiments show that the beam may buckle (in the sense of an Euler column) when the uniform magnetic field strength reaches a critical value. A mathematical model is proposed with distributed magnetic torques along the plate. A nontrivial adjacent equilibrium configuration satisfying the magnetostatic field equations is shown to exist for characteristic values of the external magnetic field. Results as predicted from this model compare favorably with experiments.

VLS Growth of Si nanowhiskers on a H-terminated Si{111} surface

1998 ◽  
Vol 536 ◽  
Author(s):  
N. Ozaki ◽  
Y. Ohno ◽  
S. Takeda ◽  
M. Hirata
Keyword(s):  
High Pressure ◽  
Growth Condition ◽  
Growth Mechanism ◽  
Quantum Confinement ◽  
Critical Value ◽  
Extended Defects ◽  
Vapor Liquid Solid ◽  
Minimum Diameter ◽  
Vls Growth ◽  
Vapor Liquid

AbstractWe have grown Si nanowhiskers on a Si{1111} surface via the vapor-liquid-solid (VLS) mechanism. The minimum diameter of the crystalline is 3nm and is close to the critical value for the effect of quantum confinement. We have found that many whiskers grow epitaxially or non-epitaxially on the substrate along the 〈112〉 direction as well as the 〈111〉 direction.In our growth procedure, we first deposited gold on a H-terminated Si{111} surface and prepared the molten catalysts of Au and Si at 500°C. Under the flow of high pressure silane gas, we have succeeded in producing the nanowhiskers without any extended defects. We present the details of the growth condition and discuss the growth mechanism of the nanowhiskers extending along the 〈112〉 direction.

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

Establishment theoretical of recommendation fertilization guide of vegetable crops in Algeria: concept and validation

2015 ◽  
Vol 5 (1) ◽  
pp. 606-620
Author(s):  
Mahtali Sbih ◽  
Zoubeir BENSID ◽  
Zohra BOUNOUARA ◽  
Fouad DJAIZ ◽  
Youcef FERRAG
Keyword(s):  
Soil Fertility ◽  
Field Experiments ◽  
Soil Analysis ◽  
Critical Value ◽  
Yield Response ◽  
Published Data ◽  
Vegetable Crops ◽  
Fertilizer Recommendation ◽  
Continuous Models ◽  
Poor Soil

The goal of fertilization is to meet the nutritional needs of plants by completing the supply of soil nutrients in an economically profitable and environmentally friendly. Achieving on-farm optimum economic crop yields of marketable quality with minimum adverse environmental impact requires close attention to fertilization guide. The recommendations seek to do this by ensuring that the available supply of plant nutrients in soil is judiciously supplemented by additions of nutrients in fertilizers. The objective is that crops must have an adequate supply of nutrients, and many crops show large and very profitable increases in yield from the correct use of fertilizers to supply nutrients. The main objective of this work is to establishing a reference guide of fertilization of vegetable crops and cereal in Algeria. To meet this objective, we have processes in two steps: 1) Establishment of theoretical fertilizer recommendation from international guide of crop fertilization; 2) Validation of these developed theoretical fertilizer recommendation by trials in the fields. Sixteen fertilization guides of vegetable crops from the Canadian provinces (5 guides), USA (10 guides) and countries of northern Europe England (1 guide). Generally, the rating of these recommendation is ranging from poor soil to soil exceedingly rich; however, the numbers of fertility classes are very different. Indeed, Quebec Ontario, Minnesota, Wisconsin New England, Maryland and Kentucky and Florida guides are subdivided into 5 fertility classes, ranging from poor soil to soil exceedingly rich. The recommendation of New Brunswick and Manitoba contain six classes. The recommendation of Michigan, Nova Scotia and England contain 10 and 7 fertility classes respectively. The recommendation fertilizer of New York and New Jersey have 3classes. Unlike the systems of fertilization recommendation mentioned above, the recommendation fertilizer of Pennsylvania is based on continuous models of P, K and contains 34 classes for P and 22 classes K. Then we standardized the P soil analysis with conversion equations (Olsen method) and units of measurement (kg/ha, mg/kg…).Following this procedure we transformed discontinued systems of fertility classes in to continuous models to facilitate comparison between the different fertilization recommendation models in one hand, in other hand to obtain critical value (CV).Finally, we used statistics of the conditional expectation in order to generate the theoretical recommendation fertilization guide of fertilization with 7 fertility classes (VL, L, M, MH, OP, H and VH). The next step was calibrating soil tests against yield responses to applied nutrient in field experiments. A database (not published data) from agriculture and agri-food Canada, were used. Production of pumpkin responded positively and significantly to P or K soil fertility levels, increases being observed with P more often than with K. According to the Cate-Nelson methods, the critical value of Olsen-P in the top 20 cm of soil was about 25 mg/kg: at values of greater than or equal to 25 mg/kg, crops achieved about 80% of their maximal yield in the absence of fertilizer application. The CV of K in soil for this crop was about 140 mg/kg. The CV found was very close to this generated by the theoretical method for recommendation of fertilization guide. Finally, we used the procedure of Cope and Rouse in both sides of the CV in order to make subdivisions of different groups of soil fertility. One calibrates the soil-test value against yield response to tile nutrient to predict fertilizer requirement.

Evaluating the security of the fiscal and budgetary system of the Kemerovo Oblast

2020 ◽  
Vol 16 (5) ◽  
pp. 966-979
Author(s):  
O.B. Sheveleva ◽  
E.V. Slesarenko
Keyword(s):  
Socioeconomic Development ◽  
Critical Value ◽  
Economic Security ◽  
Energy Market ◽  
High Tech ◽  
Regional Competitiveness ◽  
Kemerovo Oblast ◽  
Manufacturing Sectors ◽  
Fiscal System ◽  
Integral Indicator

Subject. The article deals with the security of the fiscal and budgetary system in resource-based regions during highly volatile prices in the global energy market external economic, political, technological and epidemiological shocks. Objectives. The study is to detect hazards in the fiscal and budgetary system of resource-based regions. Such hazards really put the regional competitiveness and economic security at peril. Methods. The article evaluates the security of the fiscal system in the Kemerovo Oblast through the integral indicator and the threshold (critical) value. Results. We found key threats to the fiscal and budgetary system of the Kemerovo Oblast, which undermine the regional competitiveness and economic security. Conclusions and Relevance. Authorities shall comprehensively attempt to create the environment for developing manufacturing sectors in the region, especially science-intensive and high-tech production enterprises by alleviating infrastructure and administrative constraints for business, raising the finance of science and innovation from the State and mobilize investors' resources, lure them to finance prioritized lines of the regional economic development. The findings and conclusions can be used to outline principles of the region's economic policy, socioeconomic development strategies of the region economy.

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