scholarly journals Multiperiodic orbits from interacting soft spots in cyclically sheared amorphous solids

2021 ◽  
Vol 7 (33) ◽  
pp. eabg7685
Author(s):  
Nathan C. Keim ◽  
Joseph D. Paulsen
Keyword(s):  
Steady State ◽  
Simple Model ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Driving Cycle ◽  
Displacement Fields ◽  
Closed Loops ◽  
Two Level Systems

When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the period of particle motions is a multiple of the period of driving, but the reasons for this behavior have remained unclear. Motivated by mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots—locations where particles rearrange under stress and that resemble two-level systems with hysteresis. We show that multiperiodic behavior can arise among just three or more soft spots that interact with each other, but in all cases it requires frustrated interactions, illuminating this otherwise elusive type of interaction. We suggest directions for seeking this signature of frustration in experiments and for achieving it in designed systems.

Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids

Soft Matter ◽  
2021 ◽  
Vol 17 (38) ◽  
pp. 8612-8623
Author(s):  
Weiwei Jin ◽  
Amit Datye ◽  
Udo D. Schwarz ◽  
Mark D. Shattuck ◽  
Corey S. O'Hern
Keyword(s):  
Displacement Field ◽  
Simple Shear ◽  
Strain Field ◽  
Local Strain ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Displacement Fields

Representation of the local strain field using Delaunay triangularization and the associated quadrupolar, non-affine displacement field for an amorphous solid undergoing athermal, quasistatic simple shear.

Mathematical modelling of salt purification by recrystallization. Countercurrent arrangement

1986 ◽  
Vol 51 (11) ◽  
pp. 2481-2488
Author(s):  
Benitto Mayrhofer ◽  
Jana Mayrhoferová ◽  
Lubomír Neužil ◽  
Jaroslav Nývlt
Keyword(s):  
Steady State ◽  
Simple Model ◽  
Mathematical Modelling ◽  
Distribution Coefficient ◽  
Mother Liquor ◽  
Equilibrium Temperature ◽  
Operating Conditions ◽  
Limiting Case

The paper presents a simple model of recrystallization with countercurrent flows of the solution and the crystals being purified. The model assumes steady-state operating conditions, an equilibrium between the outlet streams of each stage, and the same equilibrium temperature and distribution coefficient for all stages. With these assumptions, the model provides the basis for analyzing the variation in the degree of purity as a function of the number of recrystallization stages. The analysis is facilitated by the use of a diagram constructed for the limiting case of perfect removal of the mother liquor from the crystals between the stages.

scholarly journals THE RICH AND THE POOR IN A SIMPLE MODEL OF GROWTH AND DISTRIBUTION

2016 ◽  
Vol 20 (7) ◽  
pp. 1934-1952 ◽  
Author(s):  
Kirill Borissov
Keyword(s):  
Economic Growth ◽  
Steady State ◽  
Simple Model ◽  
Disposable Income ◽  
State Equilibrium ◽  
Positional Concerns ◽  
The Poor ◽  
The Rich ◽  
Intertemporal Equilibrium ◽  
Unique Steady State

We consider a model of economic growth with altruistic agents who care about their consumption and the disposable income of their offspring. The agents' consumption and the offspring's disposable income are subject to positional concerns. We show that, if the measure of consumption-related positional concerns is sufficiently low and/or the measure of offspring-related positional concerns is sufficiently high, then there is a unique steady-state equilibrium, which is characterized by perfect income and wealth equality, and all intertemporal equilibira converge to it. Otherwise, in steady-state equilibria, the population splits into two classes, the rich and the poor; under this scenario, in any intertemporal equilibrium, all capital is eventually owned by the households that were the wealthiest from the outset and all other households become poor.

Development of the Grain Size Distribution During the Crystallization of an Amorphous Solid

2011 ◽  
Vol 1308 ◽  
Author(s):  
Andreas Bill ◽  
Ralf B. Bergmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Growth Rates ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Nucleation And Growth ◽  
Analytic Description ◽  
Silicon Thin Films ◽  
Random Nucleation

ABSTRACTWe present an overview of the theory developed over the last few years to describe the crystallization of amorphous solids. The microstructure of the crystallizing solid is described in terms of the grain size distribution (GSD). We propose a partial differential equation that captures the physics of crystallization in random nucleation and growth processes. The analytic description is derived for isotropic and anisotropic growth rates and allows for the analysis of different stages of crystallization, from early to full crystallization. We show how the timedependence of effective nucleation and growth rates affect the final distribution. In particular, we demonstrate that for cases described by the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model applicable to a large class of crystallization processes a lognormal type distribution is obtained at full crystallization. The application of the theory to the crystallization of silicon thin films is discussed.

Macroscopic theory of dielectric solids. I. The model of molecular optics

1977 ◽  
Vol 55 (24) ◽  
pp. 2169-2179 ◽  
Author(s):  
J. E. Sipe
Keyword(s):  
Constitutive Relations ◽  
Pair Correlation ◽  
Finite Size ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Uniform Density ◽  
Macroscopic Theory ◽  
Standard Result ◽  
Dielectric Solids ◽  
Spatially Varying

An improved derivation is given of the macroscopic electrodynamic equations for dielectric solids of finite size composed of molecules with a given polarizability, α = α(ω), interacting only via the retarded dipole–dipole coupling. We present a derivation of the constitutive relations for both crystalline and amorphous solids, which is not based on an expansion in powers of α, and in which the radiative reaction forces are carefully taken into account. The spatially varying density and pair correlation function of an amorphous solid, defined with the help of spatial averaging procedures, are shown to satisfy an integral 'counting' relation, which puts a condition on any physically consistent model of an amorphous solid. In the absence of dissipative damping, a medium is shown to be characterized by a real, in general spatially varying, dielectric constant. For solids of uniform density, crystalline or amorphous, we obtain the standard result that inside such a medium light propagates without scattering. For amorphous solids with varying density, the theory forms the basis of the macroscopic theory of light scattering from density in-homogeneities.

Filtration efficiency and pressure drop modelling of particulate filters with rear plug damage

2020 ◽  
pp. 146808742091667
Author(s):  
Onoufrios Haralampous ◽  
Marios Mastrokalos ◽  
Fotini Tzorbatzoglou ◽  
Chris Dritselis
Keyword(s):  
Steady State ◽  
Pressure Drop ◽  
Filtration Efficiency ◽  
Driving Cycle ◽  
Ceramic Filter ◽  
Particulate Filter ◽  
Local Pressure ◽  
Particulate Filters ◽  
Pressure Loss Coefficient ◽  
Particulate Mass

A model suitable for wall-flow particulate filters with partial rear plug damage is developed and experimentally validated in this work. A ceramic filter with 16% of the rear plugs mechanically removed is tested at steady-state conditions on the engine bench and transient driving cycle conditions on the chassis dynamometer. After decanning of the monolith, destructive analysis is conducted to identify deposit loading variations and scanning electron microscopy is used to study the deposit structures in the channels. It is shown that channels without rear plugs develop distinct deposit structures in the entry zone. Hence, a local pressure loss coefficient is applied to model the effect of entrance flow constrictions, taking also into account deposit restructuring phenomena at higher flow rates. In addition, a deep-bed filtration submodel is used to capture the effect of non-uniform wall velocities on deposit accumulation in the wall. The modified model is first fitted to the engine bench data and then validated in a wider range of conditions using the driving cycle tests. With the exception of prolonged steady-state loading conditions, good pressure drop and filtration efficiency predictions are obtained throughout the tests in conjunction with correct deposit property profiles. Notably, the cold-start worldwide harmonized light vehicles test cycle shows that the current European on-board diagnosis threshold limit for particulate mass is too relaxed to trigger a malfunction indication for moderate filter faults. In conclusion, the model can be applied in damaged particulate filter studies for the assessment of leaked particulate mass, the specification of more effective legislation limits and the development of rigorous on-board diagnosis systems and algorithms.

GLASSY BEHAVIOR OF YBa2Cu3O7

1988 ◽  
Vol 02 (11n12) ◽  
pp. 1327-1333 ◽  
Author(s):  
A. SAHLING ◽  
S. SAHLING
Keyword(s):  
Heat Capacity ◽  
Temperature Dependence ◽  
Density Of States ◽  
Equilibrium Temperature ◽  
Amorphous Solids ◽  
Acoustic Measurements ◽  
Rapid Cooling ◽  
Glassy Behavior ◽  
Long Time ◽  
Two Level Systems

Long time power released in YBa 2 Cu 3 O 7 after rapid cooling from equilibrium temperature T1 (2.35 K≤T≤15.11 K ) to T0=1.5 K and heat capacity (1.2 K ≤T≤100 K ) were measured. The observed time and temperature dependence of the power release is similar to those of amorphous solids. The resulting density of states of two-level systems is close to the values obtained from heat capacity and acoustic measurements.

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