scholarly journals Self-similar pattern formation and continuous mechanics of self-similar systems

2007 ◽  
Vol 11 (2) ◽  
pp. 665-676 ◽  
Author(s):  
A. V. Dyskin
Keyword(s):  
Pattern Formation ◽  
Crack Growth ◽  
Similar Pattern ◽  
Similar Distribution ◽  
Parallel Cracks ◽  
Element Size ◽  
Self Similar ◽  
The Stability ◽  
Further Development ◽  
The Continuum

Abstract. In many cases, the critical state of systems that reached the threshold is characterised by self-similar pattern formation. We produce an example of pattern formation of this kind – formation of self-similar distribution of interacting fractures. Their formation starts with the crack growth due to the action of stress fluctuations. It is shown that even when the fluctuations have zero average the cracks generated by them could grow far beyond the scale of stress fluctuations. Further development of the fracture system is controlled by crack interaction leading to the emergence of self-similar crack distributions. As a result, the medium with fractures becomes discontinuous at any scale. We develop a continuum fractal mechanics to model its physical behaviour. We introduce a continuous sequence of continua of increasing scales covering this range of scales. The continuum of each scale is specified by the representative averaging volume elements of the corresponding size. These elements determine the resolution of the continuum. Each continuum hides the cracks of scales smaller than the volume element size while larger fractures are modelled explicitly. Using the developed formalism we investigate the stability of self-similar crack distributions with respect to crack growth and show that while the self-similar distribution of isotropically oriented cracks is stable, the distribution of parallel cracks is not. For the isotropically oriented cracks scaling of permeability is determined. For permeable materials (rocks) with self-similar crack distributions permeability scales as cube of crack radius. This property could be used for detecting this specific mechanism of formation of self-similar crack distributions.

scholarly journals Self-similar pattern formation and continuous mechanics of self-similar systems

2006 ◽  
Vol 3 (4) ◽  
pp. 1879-1913
Author(s):  
A. V. Dyskin
Keyword(s):  
Pattern Formation ◽  
Crack Growth ◽  
Similar Pattern ◽  
Effective Characteristics ◽  
Similar Distribution ◽  
Fracture System ◽  
Self Similar ◽  
The Stability ◽  
Further Development ◽  
The Continuum

Abstract. In many cases, the critical state of systems that reached the threshold is characterised by self-similar pattern formation. We produce an example of pattern formation of this kind – formation of self-similar distribution of interacting fractures. The driving force of the fracture system formation is the crack growth due to the action of stress fluctuations. The importance of this mechanism is that even when the fluctuations have zero average the cracks generated by them could growth far beyond the scale of stress fluctuations. Further development of the fracture system is controlled by crack interaction, which in the case of isotropically oriented cracks leads to the emergence of self-similar distributions. The presence of self-similar distributions of fractures in a material poses a challenge in continuum modelling, since this material becomes discontinuous at any scale. We develop a continuum fractal mechanics to model mechanical behaviour of such materials. We introduce a continuous sequence of continua of increasing scales covering this range of scales. The continuum of each scale is specified by the representative volume elements of the corresponding size over which averaging is performed in the process of defining the field variables in the continuum. Subsequently, at each scale the material is modelled by a continuum that hides the cracks of smaller scales while explicitly introducing larger structural elements. The properties assigned to the continuum are effective characteristics accounting for the macroscopic effect of the hidden cracks. Using the developed formalism we investigate the stability of self-similar crack distributions with respect to crack growth and show that while the self-similar distribution of isotropically oriented cracks is stable, the distribution of parallel cracks is not. For the isotropically oriented cracks scaling of permeability is determined. For the crack distribution produced by the action of stress fluctuations permeability increases as cube of crack radius. This property could be used for detecting this specific mechanism of formation of self-similar crack distributions.

The stability of dislocation networks under various oxygen-doping conditions in superconducting Bi2Sr2CaCu2Oy single crystals and their influence on the flux pinning properties

1994 ◽  
Vol 52 ◽  
pp. 802-803
Author(s):  
Y. Feng ◽  
X. Y. Cai ◽  
R. J. Kelley ◽  
D. C. Larbalestier
Keyword(s):  
Single Crystals ◽  
Oxygen Content ◽  
Basal Plane ◽  
Flux Pinning ◽  
Pinning Centers ◽  
Before And After ◽  
Anomalous Peak ◽  
Basal Plane Dislocation ◽  
The Stability ◽  
Further Development

The issue of strong flux pinning is crucial to the further development of high critical current density Bi-Sr-Ca-Cu-O (BSCCO) superconductors in conductor-like applications, yet the pinning mechanisms are still much debated. Anomalous peaks in the M-H (magnetization vs. magnetic field) loops are commonly observed in Bi2Sr2CaCu2Oy (Bi-2212) single crystals. Oxygen vacancies may be effective flux pinning centers in BSCCO, as has been found in YBCO. However, it has also been proposed that basal-plane dislocation networks also act as effective pinning centers. Yang et al. proposed that the characteristic scale of the basal-plane dislocation networksmay strongly depend on oxygen content and the anomalous peak in the M-H loop at ˜20-30K may be due tothe flux pinning of decoupled two-dimensional pancake vortices by the dislocation networks. In light of this, we have performed an insitu observation on the dislocation networks precisely at the same region before and after annealing in air, vacuumand oxygen, in order to verify whether the dislocation networks change with varying oxygen content Inall cases, we have not found any noticeable changes in dislocation structure, regardless of the drastic changes in Tc and the anomalous magnetization. Therefore, it does not appear that the anomalous peak in the M-H loops is controlled by the basal-plane dislocation networks.

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Golam Mortuja Sarkar ◽  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Friction Coefficient ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Hiemenz Flow ◽  
Self Similar ◽  
The Stability

Purpose This paper aims to theoretically and numerically investigate the steady two-dimensional (2D) Hiemenz flow with heat transfer of Reiner-Rivlin fluid over a linearly stretching/shrinking sheet. Design/methodology/approach The Navier–Stokes equations are transformed into self-similar equations using appropriate similarity transformations and then solved numerically by using shooting technique. A simple but effective mathematical analysis has been used to prove the existence of a solution for stretching case (λ> 0). Moreover, an attempt has been laid to carry the asymptotic solution behavior for large stretching. The obtained asymptotic solutions are compared with direct numerical solutions, and the comparison is quite remarkable. Findings It is observed that the self-similar equations exhibit dual solutions within the range [λc, −1] of shrinking parameter λ, where λc is the turning point from where the dual solutions bifurcate. Unique solution is found for all stretching case (λ > 0). It is noticed that the effects of cross-viscous parameter L and shrinking parameter λ on velocity and thermal fields show opposite character in the dual solution branches. Thus, a linear temporal stability analysis is performed to determine the basic feasible solution. The stability analysis is based on the sign of the smallest eigenvalue, where positive or negative sign leading to a stable or unstable solution. The stability analysis reveals that the first solution is stable that describes the main flow. Increase in cross-viscous parameter L resulting in a significant increment in skin friction coefficient, local Nusselt number and dual solutions domain. Originality/value This work’s originality is to examine the combined effects of cross-viscous parameter and stretching/shrinking parameter on skin friction coefficient, local Nusselt number, velocity and temperature profiles of Hiemenz flow over a stretching/shrinking sheet. Although many studies on viscous fluid and nanofluid have been investigated in this field, there are still limited discoveries on non-Newtonian fluids. The obtained results can be used as a benchmark for future studies of higher-grade non-Newtonian flows with several physical aspects. All the generated results are claimed to be novel and have not been published elsewhere.

Stability of the Professional Development Assessment

1997 ◽  
Vol 84 (3_suppl) ◽  
pp. 1373-1374
Author(s):  
Jack Kasar
Keyword(s):  
Professional Development ◽  
Occupational Therapy ◽  
Professional Behaviors ◽  
The Stability ◽  
Development Assessment ◽  
Further Development

The Professional Development Assessment was constructed and pilot-tested with 76 students in three occupational therapy programs. A comparison of pretest and posttest scores yielded a significant correlation of .48, supporting the stability of responding over 1 to 2 years and suggesting usefulness of further development for evaluation of professional behaviors in students.

scholarly journals Устойчивость углеродной нанолуковицы в контакте с графитовой подложкой

2019 ◽  
Vol 45 (12) ◽  
pp. 9
Author(s):  
С.Ш. Рехвиашвили ◽  
М.М. Бухурова
Keyword(s):  
Theoretical Model ◽  
Interaction Potential ◽  
Interatomic Interaction ◽  
Continuum Approximation ◽  
Graphite Phase ◽  
Interatomic Interaction Potential ◽  
The Stability ◽  
The Continuum

AbstractA theoretical model describing the stability of a carbon nano-onion in the presence of a bulk catalytic graphite phase is constructed based on the continuum approximation of interatomic interaction potential and mechanics of deformed systems. It is shown that a carbon nano-onion becomes unstable when its radius exceeds double value of the radius of a fullerene C_60 molecule.

scholarly journals The X-Ray Nova GRO J0422+32 in Decline and Quiescence

1996 ◽  
Vol 158 ◽  
pp. 399-400
Author(s):  
M. R. Garcia ◽  
P. J. Callanan ◽  
J. E. McClintock ◽  
P. Zhao
Keyword(s):  
Emission Line ◽  
Emission Region ◽  
Dwarf Novae ◽  
X Ray ◽  
First Order ◽  
Band Emission ◽  
Line Region ◽  
Hα Emission ◽  
The Stability ◽  
The Continuum

We have followed the X-ray nova GRO J0422+32, spectroscopically and photometrically, throughout the decline to quiescence.In the final stages of decay (days 430…880 after the outburst, see Callanan et al. (1995) for the epoch 1995), the equivalent width (EW) of the Hα emission increases monotonically and the R magnitude decreases monotonically. This suggests that the flux in the Hα line is constant, while the continuum fades. The Hα flux is the product of the R band flux (F(R), arbitrarily scaled to 100 at R = 19 mag) and the EW, and is shown in the last column of the table below. The Hα flux varies by only ~ 30% while the continuum fades by a factor of eight (from R = 19 mag to R = 21.3 mag). So, to first order, the Hα luminosity is constant in the final stages of decay. While it is generally the case that the emission line EWs in individual dwarf novae also increase during the decay, the exact behavior seen in GRO J0422+32 is not what is seen for dwarf novae (on average). Using the relation between EW[Hβ] and Mv given in figure 6 of Patterson (1984), we would expect a factor of ~ 5 variation in the Hα flux during days 430…880. The stability of the Hα flux implies that somehow the emission line region is ‘disconnected’ from the continuum (R–band) emission region.

scholarly journals Traveling and standing waves mediate pattern formation in cellular protrusions

2020 ◽  
Vol 6 (32) ◽  
pp. eaay7682
Author(s):  
Sayak Bhattacharya ◽  
Tatsat Banerjee ◽  
Yuchuan Miao ◽  
Huiwang Zhan ◽  
Peter N. Devreotes ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Traveling Waves ◽  
Standing Waves ◽  
Cell Cortex ◽  
Theoretical Studies ◽  
Direct Transformation ◽  
Diffusion Parameters ◽  
Excitable Systems ◽  
Mutant Strains ◽  
The Stability

The mechanisms regulating protrusions during amoeboid migration exhibit excitability. Theoretical studies have suggested the possible coexistence of traveling and standing waves in excitable systems. Here, we demonstrate the direct transformation of a traveling into a standing wave and establish conditions for the stability of this conversion. This theory combines excitable wave stopping and the emergence of a family of standing waves at zero velocity, without altering diffusion parameters. Experimentally, we show the existence of this phenomenon on the cell cortex of some Dictyostelium and mammalian mutant strains. We further predict a template that encompasses a spectrum of protrusive phenotypes, including pseudopodia and filopodia, through transitions between traveling and standing waves, allowing the cell to switch between excitability and bistability. Overall, this suggests that a previously-unidentified method of pattern formation, in which traveling waves spread, stop, and turn into standing waves that rearrange to form stable patterns, governs cell motility.

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