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.

GROSS–WITTEN POINT AND DECONFINEMENT

2005 ◽  
Vol 20 (19) ◽  
pp. 4469-4474 ◽  
Author(s):  
ROBERT D. PISARSKI
Keyword(s):  
Phase Transition ◽  
Gauge Theory ◽  
Critical Point ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
First Order

Following Aharony et al., we analyze the deconfining phase transition in a SU(∞) gauge theory in mean field approximation. The Gross–Witten model emerges as an "ultra"-critical point for deconfinement: while thermodynamically of first order, masses vanish, asymmetrically, at the transition. Potentials for N = 3 are also shown.

scholarly journals Two exactly soluble models of rigidity percolation

2014 ◽  
Vol 372 (2008) ◽  
pp. 20120038 ◽  
Author(s):  
M. F. Thorpe ◽  
R. B. Stinchcombe
Keyword(s):  
Scaling Laws ◽  
Mean Field ◽  
Approximate Methods ◽  
First Order ◽  
Rigidity Percolation ◽  
Bethe Lattices ◽  
Cluster Geometry ◽  
Pebble Game ◽  
Lattice Dimension

We summarize results for two exactly soluble classes of bond-diluted models for rigidity percolation, which can serve as a benchmark for numerical and approximate methods. For bond dilution problems involving rigidity, the number of floppy modes F plays the role of a free energy. Both models involve pathological lattices with two-dimensional vector displacements. The first model involves hierarchical lattices where renormalization group calculations can be used to give exact solutions. Algebraic scaling transformations produce a transition of the second order, with an unstable critical point and associated scaling laws at a mean coordination 〈 r 〉=4.41, which is above the ‘mean field’ value 〈 r 〉=4 predicted by Maxwell constraint counting. The order parameter exponent associated with the spanning rigid cluster geometry is β =0.0775 and that associated with the divergence of the correlation length and the anomalous lattice dimension d is dν =3.533. The second model involves Bethe lattices where the rigidity transition is massively first order by a mean coordination 〈 r 〉=3.94 slightly below that predicted by Maxwell constraint counting. We show how a Maxwell equal area construction can be used to locate the first-order transition and how this result agrees with simulation results on larger random-bond lattices using the pebble game algorithm.

Phase transition and universality of the three-one spin interaction based on the majority-rule model

2021 ◽  
pp. 2150115
Author(s):  
Roni Muslim ◽  
Rinto Anugraha ◽  
Sholihun Sholihun ◽  
Muhammad Farchani Rosyid
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Majority Rule ◽  
Mean Field ◽  
Opinion Dynamics ◽  
Universality Class ◽  
Spin Interaction ◽  
Population Number ◽  
Infinite Population ◽  
Rule Model

In this work, we study the opinion dynamics of majority-rule model on a complete graph with additional social behavior namely anticonformity. We consider four spins with three-one interaction; three spins persuade the fourth spin in the population. We perform analytical and numerical calculations to find the critical behavior of the system. From both, we obtained the agreement results, e.g. the system undergoes a second-order phase transition and the critical point of the system only depends on the population number. In addition, the critical point decays exponentially as the number population increases. For the infinite population, the obtained critical point is [Formula: see text], which agrees well with that of the previous work. We also obtained the critical exponents [Formula: see text] and [Formula: see text] of the model, thus, the model is in the same universality class with the mean-field Ising.

Phase transition of the Sznajd model with anticonformity for two different agent configurations

2020 ◽  
Vol 31 (04) ◽  
pp. 2050052 ◽  
Author(s):  
Roni Muslim ◽  
Rinto Anugraha ◽  
Sholihun Sholihun ◽  
Muhammad Farchani Rosyid
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Mean Field ◽  
Opinion Dynamics ◽  
Universality Class ◽  
Consensus Process ◽  
The Social ◽  
The Mean ◽  
Analytical Result ◽  
Fully Connected

In this work, we study the opinion dynamics of the Sznajd model with anticonformity on a fully-connected network. We consider four agents with two different configurations; three against one (3–1) and two against two (2–2). We consider two different individual behaviors, conformity and anticonformity, and observe the effect on the critical behavior of the model. We analyze the differences between the phase transitions that occur for both agent configurations. We find that both agent configurations have a different critical point. The critical point of the 3–1 agent is smaller than that of the 2–2 agent configuration. From the simulation and analytical result, we find that the critical point for the 3–1 occurs at [Formula: see text], and for the 2–2, at [Formula: see text]. From the social viewpoint, the consensus process in a population is faster with a larger influencer in the same number of small group of the population. In addition, we find the critical exponents for both configurations are the same, that are [Formula: see text] and [Formula: see text]. Our results suggest that both models are identical and in the mean-field Ising universality class.

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 The quark-meson model and the phase diagram of QCD

2020 ◽  
Vol 15 ◽  
pp. 15
Author(s):  
N. Tetradis
Keyword(s):  
Phase Diagram ◽  
Renormalization Group ◽  
Critical Point ◽  
Mean Field Theory ◽  
Mean Field ◽  
Universality Class ◽  
Quark Masses ◽  
Qcd Phase Diagram ◽  
Group I ◽  
Exact Renormalization Group

I discuss the QCD phase diagram in the context of the linear quark-meson model with two flavours, using the exact renormalization group. I first give a pedagogical derivation of the qualitative features of the phase diagram based on mean field theory. Then I summarize how the the universality classes of the second-order phase transitions can be determined through the exact renormalization group. For non-zero quark masses I explain how the universal equation of state of the Ising universality class can be used in order to describe the physical behaviour near the critical point. The effective exponents that parametrize the growth of physical quantities, such as the correlation length, are given by combinations of the critical exponents of the Ising class that depend on the path along which the critical point is approached. In general the critical region, in which such quantities become large, is smaller than naively expected.

scholarly journals Gliding Down the QCD Transition Line, from Nf = 2 till the Onset of Conformality

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1833
Author(s):  
Andrey Yu Kotov ◽  
Maria Paola Lombardo ◽  
Anton Trunin
Keyword(s):  
Coupling Strength ◽  
Critical Line ◽  
Mean Field ◽  
Universality Class ◽  
Transition Line ◽  
First Order ◽  
Conformal Window ◽  
Singular Behaviour ◽  
First Order Transition ◽  
Field Behaviour

We review the hot QCD transition with varying number of flavours, from two till the onset of the conformal window. We discuss the universality class for Nf=2, along the critical line for two massless light flavours, and a third flavour whose mass serves as an interpolator between Nf=2 and Nf=3. We identify a possible scaling window for the 3D O(4) universality class transition, and its crossover to a mean field behaviour. We follow the transition from Nf=3 to larger Nf, when it remains of first order, with an increasing coupling strength; we summarise its known properties, including possible cosmological applications as a model for a strong electroweak transition. The first order transition, and its accompanying second order endpoint, finally morphs into the essential singularity at the onset of the conformal window, following the singular behaviour predicted by the functional renormalisation group.

Receptions of the Past: Commemoration, Racism, Desire

Somatechnics ◽  
2017 ◽  
Vol 7 (2) ◽  
pp. 288-303
Author(s):  
Michael Connors Jackman
Keyword(s):  
Critical Point ◽  
Social Relations ◽  
White Privilege ◽  
Body Politic ◽  
The Body ◽  
Race And Racism ◽  
Lesbian And Gay ◽  
The Past ◽  
History Of

This article investigates the ways in which the work of The Body Politic (TBP), the first major lesbian and gay newspaper in Canada, comes to be commemorated in queer publics and how it figures in the memories of those who were involved in producing the paper. In revisiting a critical point in the history of TBP from 1985 when controversy erupted over race and racism within the editorial collective, this discussion considers the role of memory in the reproduction of whiteness and in the rupture of standard narratives about the past. As the controversy continues to haunt contemporary queer activism in Canada, the productive work of memory must be considered an essential aspect of how, when and for what reasons the work of TBP comes to be commemorated. By revisiting the events of 1985 and by sifting through interviews with individuals who contributed to the work of TBP, this article complicates the narrative of TBP as a bluntly racist endeavour whilst questioning the white privilege and racially-charged demands that undergird its commemoration. The work of producing and preserving queer history is a vital means of challenging the intentional and strategic erasure of queer existence, but those who engage in such efforts must remain attentive to the unequal terrain of social relations within which remembering forms its objects.

Exploring Baryon Rich Matter with Heavy-Ion Collisions

2019 ◽  
Vol 64 (7) ◽  
pp. 583 ◽  
Author(s):  
S. Harabasz
Keyword(s):  
Center Of Mass ◽  
Heavy Ion ◽  
State Density ◽  
Heavy Nuclei ◽  
First Order ◽  
Center Of Mass Energy ◽  
Ion Collisions ◽  
Deconfinement Phase Transition ◽  
Ground State Density

Collisions of heavy nuclei at (ultra-)relativistic energies provide a fascinating opportunity to re-create various forms of matter in the laboratory. For a short extent of time (10-22 s), matter under extreme conditions of temperature and density can exist. In dedicated experiments, one explores the microscopic structure of strongly interacting matter and its phase diagram. In heavy-ion reactions at SIS18 collision energies, matter is substantially compressed (2–3 times ground-state density), while moderate temperatures are reached (T < 70 MeV). The conditions closely resemble those that prevail, e.g., in neutron star mergers. Matter under such conditions is currently being studied at the High Acceptance DiElecton Spectrometer (HADES). Important topics of the research program are the mechanisms of strangeness production, the emissivity of matter, and the role of baryonic resonances herein. In this contribution, we will focus on the important experimental results obtained by HADES in Au+Au collisions at 2.4 GeV center-of-mass energy. We will also present perspectives for future experiments with HADES and CBM at SIS100, where higher beam energies and intensities will allow for the studies of the first-order deconfinement phase transition and its critical endpoint.

The Role of Hydrophobicity in the Stability and pH-Switchability of (RXDX)4 and Coumarin-RXDX Conjugate β-Sheets

2020 ◽  
Author(s):  
Ryan Weber ◽  
Martin McCullagh
Keyword(s):  
Biological Imaging ◽  
Ph Sensing ◽  
Hydrophobic Residue ◽  
Ideal Candidate ◽  
Self Assembling ◽  
Sensing Applications ◽  
Β Sheets ◽  
The Stability ◽  
Dynamics Simulations

<p>pH-switchable, self-assembling materials are of interest in biological imaging and sensing applications. Here we propose that combining the pH-switchability of RXDX (X=Ala, Val, Leu, Ile, Phe) peptides and the optical properties of coumarin creates an ideal candidate for these materials. This suggestion is tested with a thorough set of all-atom molecular dynamics simulations. We first investigate the dependence of pH-switchabiliy on the identity of the hydrophobic residue, X, in the bare (RXDX)<sub>4</sub> systems. Increasing the hydrophobicity stabilizes the fiber which, in turn, reduces the pH-switchabilty of the system. This behavior is found to be somewhat transferable to systems in which a single hydrophobic residue is replaced with a coumarin containing amino acid. In this case, conjugates with X=Ala are found to be unstable and both pHs while conjugates with X=Val, Leu, Ile and Phe are found to form stable β-sheets at least at neutral pH. The (RFDF)<sub>4</sub>-coumarin conjugate is found to have the largest relative entropy value of 0.884 +/- 0.001 between neutral and acidic coumarin ordering distributions. Thus, we posit that coumarin-(RFDF)<sub>4</sub> containing peptide sequences are ideal candidates for pH-sensing bioelectronic materials.</p>

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