Interaction of Public and Private Enforcement

OʼConnor, Kevin; Renfro, Hannah L.; Briggs, Adam C.

doi:10.4337/9781849808088.00020

Cited by 5 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the mapping to hydrocarbons in the previous paragraph, one finds f b = 240u 0 /a ∼ 3nN. This is comparable to experimental estimates [42,43] and density functional theory results (∼ 6nN) for the force needed to break pentane backbone bonds [44]. Simulations with a range of potentials show that the breaking force is the most important aspect of the potential and its influence is discussed briefly in Sec.…”

Section: A Simulation Modelsupporting

confidence: 72%

Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength

Robbins

Perahia

et al. 2014

Phys. Rev. E

View full text Add to dashboard Cite

Self-healing of polymer films often takes place as the molecules diffuse across a damaged region, above their melting temperature. Using molecular dynamics simulations we probe the healing of polymer films and compare the results with those obtained for thermal welding of homopolymer slabs. These two processes differ from each other in their interfacial structure since damage leads to increased polydispersity and more short chains. A polymer sample was cut into two separate films that were then held together in the melt state. The recovery of the damaged film was followed as time elapsed and polymer molecules diffused across the interface. The mass uptake and formation of entanglements, as obtained from primitive path analysis, are extracted and correlated with the interfacial strength obtained from shear simulations. We find that the diffusion across the interface is significantly faster in the damaged film compared to welding because of the presence of short chains. Though interfacial entanglements increase more rapidly for the damaged films, a large fraction of these entanglements are near chain ends. As a result, the interfacial strength of the healing film increases more slowly than for welding. For both healing and welding, the interfacial strength saturates as the bulk entanglement density is recovered across the interface. However, the saturation strength of the damaged film is below the bulk strength for the polymer sample. At saturation, cut chains remain near the healing interface. They are less entangled and as a result they mechanically weaken the interface. Chain stiffness increases the density of entanglements, which increases the strength of the interface. Our results show that a few entanglements across the interface are sufficient to resist interfacial chain pullout and enhance the mechanical strength.

show abstract

Section: A Simulation Modelsupporting

confidence: 72%

Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength

Robbins

Perahia

et al. 2014

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…In fact it turns out that the lower critical point (4.8) can be reproduced from the effective potential for the scalar mode on the fuzzy sphere [70] as 3…”

Section: The Lower Critical Point and The 'One-loop Dominance'mentioning

confidence: 99%

“…, whereas the upper critical point behaves as α (u) cr ∼ 0.66 at large N . The position of the lower critical point can be reproduced by considering the effective potential for the scalar mode on the fuzzy sphere[70].…”

mentioning

confidence: 99%

Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term

Azuma

Bal

Nagao

et al. 2004

J. High Energy Phys.

153

View full text Add to dashboard Cite

Fuzzy spheres appear as classical solutions in a matrix model obtained via dimensional reduction of 3-dimensional Yang-Mills theory with the Chern-Simons term. Well-defined perturbative expansion around these solutions can be formulated even for finite matrix size, and in the case of k coincident fuzzy spheres it gives rise to a regularized U(k) gauge theory on a noncommutative geometry. Here we study the matrix model nonperturbatively by Monte Carlo simulation. The system undergoes a first order phase transition as we change the coefficient (α) of the Chern-Simons term. In the small α phase, the large N properties of the system are qualitatively the same as in the pure Yang-Mills model (α = 0), whereas in the large α phase a single fuzzy sphere emerges dynamically. Various 'multi fuzzy spheres' are observed as meta-stable states, and we argue in particular that the k coincident fuzzy spheres cannot be realized as the true vacuum in this model even in the large N limit. We also perform one-loop calculations of various observables for arbitrary k including k = 1. Comparison with our Monte Carlo data suggests that higher order corrections are suppressed in the large N limit.

show abstract

“…Motivated by the work [57,58] it was conjectured [66] that the joint eigenvalues distribution of d matrices X 1 , X 2 ,...X d with dynamics given by a reduced Yang-Mills action should be uniform inside a solid ball of some radius R. We have already checked that this conjecture works in three dimensions [59]. We will check now that this conjecture holds also true in four dimensions.…”

Section: Eigenvalues Distributionsmentioning

confidence: 82%

Impact of Supersymmetry on Emergent Geometry in Yang–mills Matrix Models Ii

Ydri

2012

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

We present a study of D = 4 supersymmetric Yang-Mills matrix models with SO(3) mass terms based on the Monte Carlo method.In the bosonic models we show the existence of an exotic first/second order transition from a phase with a well defined background geometry (the fuzzy sphere) to a phase with commuting matrices with no geometry in the sense of Connes. At the transition point the sphere expands abruptly to infinite size then it evaporates as we increase the temperature (the gauge coupling constant). The transition looks first order due to the discontinuity in the action whereas it looks second order due to the divergent peak in the specific heat.The fuzzy sphere is stable for the supersymmetric models in the sense that the bosonic phase transition is turned into a very slow crossover transition. The transition point is found to scale to zero with N . We conjecture that the transition from the background sphere to the phase of commuting matrices is associated with spontaneous supersymmetry breaking.The eigenvalues distribution of any of the bosonic matrices in the matrix phase is found to be given by a non-polynomial law obtained from the fact that the joint probability distribution of the four matrices is uniform inside a solid ball with radius R. The eigenvalues of the gauge field on the background geometry are also found to be distributed according to this non-polynomial law. *

show abstract

Interaction of Public and Private Enforcement

Cited by 5 publications

References 0 publications

Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength

Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength

Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term

Impact of Supersymmetry on Emergent Geometry in Yang–mills Matrix Models Ii

Contact Info

Product

Resources

About