scholarly journals Discontinuous yielding transition of amorphous materials with low bulk modulus

2021 ◽  
Vol 2021 (12) ◽  
pp. 123201
Author(s):  
E A Jagla
Keyword(s):  
Shear Band ◽  
Bulk Modulus ◽  
Amorphous Materials ◽  
Mean Field ◽  
Constant Strain Rate ◽  
Two Dimensional ◽  
Coexistence Region ◽  
Relative Value ◽  
Hamiltonian Model

Abstract The yielding transition of amorphous materials is studied with a two-dimensional Hamiltonian model that allows both shear and volume deformations. The model is investigated as a function of the relative value of the bulk modulus B with respect to the shear modulus μ. When the ratio B/μ is small enough, the yielding transition becomes discontinuous, yet reversible. If the system is driven at constant strain rate in the coexistence region, a spatially localized shear band is observed while the rest of the system remains blocked. The crucial role of volume fluctuations in the origin of this behavior is clarified in a mean field version of the model.

scholarly journals Effect of weak disorder on the BCS–BEC crossover in a two-dimensional Fermi gas

2017 ◽  
Vol 31 (09) ◽  
pp. 1750066
Author(s):  
Ayan Khan ◽  
B. Tanatar
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fermi Gas ◽  
Ultracold Fermi Gas ◽  
Condensate Fraction ◽  
Two Dimensional ◽  
Weak Disorder ◽  
Unique Nature

In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the framework of mean-field theory where the impurity is introduced through Gaussian fluctuations. We have investigated the role of the impurity by studying the experimentally accessible quantities such as condensate fraction and equation of state of the ultracold systems. Our analysis reveals that at the crossover, the disorder enhances superfluidity, which we attribute to the unique nature of the unitary region and to the dimensional effect.

scholarly journals Random critical point separates brittle and ductile yielding transitions in amorphous materials

2018 ◽  
Vol 115 (26) ◽  
pp. 6656-6661 ◽  
Author(s):  
Misaki Ozawa ◽  
Ludovic Berthier ◽  
Giulio Biroli ◽  
Alberto Rosso ◽  
Gilles Tarjus
Keyword(s):  
Critical Point ◽  
Amorphous Materials ◽  
Mean Field ◽  
Universality Class ◽  
Particle Interactions ◽  
Molecular Glasses ◽  
First Order ◽  
Initial Stability ◽  
Dynamics Simulations

We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behaviors found in amorphous materials does not necessarily result from the diversity of particle interactions or microscopic dynamics but is instead unified by carefully considering the role of the initial stability of the system.

scholarly journals Role of fluctuations in the yielding transition of two-dimensional glasses

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Misaki Ozawa ◽  
Ludovic Berthier ◽  
Giulio Biroli ◽  
Gilles Tarjus
Keyword(s):  
Two Dimensional

scholarly journals Filaments and the Solar Dynamo

1998 ◽  
Vol 167 ◽  
pp. 406-414
Author(s):  
N. Seehafer
Keyword(s):  
Mean Field ◽  
Decisive Role ◽  
Dynamo Theory ◽  
Simultaneous Generation ◽  
Alpha Effect ◽  
Generation Region ◽  
The Mean ◽  
Numerical Bifurcation ◽  
Dynamo Effect

AbstractFilaments are a global phenomenon and their formation, structure and dynamics are determined by magnetic fields. So they are an important signature of the solar magnetism. The central mechanism in traditional mean-field dynamo theory is the alpha effect and it is a major result of this theory that the presence of kinetic or magnetic helicities is at least favourable for the effect. Recent studies of the magnetohydrodynamic equations by means of numerical bifurcation-analysis techniques have confirmed the decisive role of helicity for a dynamo effect. The alpha effect corresponds to the simultaneous generation of magnetic helicities in the mean field and in the fluctuations, the generation rates being equal in magnitude and opposite in sign. In the case of statistically stationary and homogeneous fluctuations, in particular, the alpha effect can increase the energy in the mean magnetic field only under the condition that also magnetic helicity is accumulated there. Generally, the two helicities generated by the alpha effect, that in the mean field and that in the fluctuations, have either to be dissipated in the generation region or to be transported out of this region. The latter may lead to the appearance of helicity in the atmosphere, in particular in filaments, and thus provide valuable information on dynamo processes inaccessible to in situ measurements.

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