Topological Defects in a Deformed Gauge Theory

In this paper, we will analyse the topological defects in a deformation of a non-abelian gauge theory using the Polyakov variables. The gauge theory will be deformed by the existence of a minimum measurable length scale in the background spacetime. We will construct the Polyakov loops for this deformed non-abelian gauge theory, and use these deformed loop space variables for obtaining a deformed loop space curvature. It will be demonstrated that this curvature will vanish if the deformed Bianchi identities are satisfied. However, it is possible that the original Bianchi identities are satisfied, but the deformed Bianchi identities are violated at the leading order in the deformation parameter, due to some topological defects. Thus, topological defects could be produced purely from a deformation of the background geometry.Comment: 16 pages, Accepted for publication in NP

Single and Paired Point Defects in a 2D Wigner Crystal

Using the path-integral Monte Carlo method, we calculate the energy to form single and pair vacancies and interstitials in a two-dimensional Wigner crystal of electrons. We confirm that the lowest-lying energy defects of a 2D electron Wigner crystal are interstitials, with a creation energy roughly 2/3 that of a vacancy. The formation energy of the defects goes to zero near melting, suggesting that point defects might mediate the melting process. In addition, we find that the interaction between defects is strongly attractive, so that most defects will exist as bound pairs.Comment: 4 pages, 5 encapsulated figure

Crashed Software: Assessing Product Liability for Software Defects in Automated Vehicles

Automated vehicles will not only redefine the role of drivers, but also present new challenges in assessing product liability. In light of the increased risks of software defects in automated vehicles, this Note will review the current legal and regulatory framework related to product liability and assess the challenges in addressing on-board software defects and cybersecurity breaches from both the consumer and manufacturer perspective. While manufacturers are expected to assume more responsibility for accidents as vehicles become fully automated, it can be difficult to determine the scope of liability regarding unexpected software defects. On the other hand, consumers face new challenges in bringing product liability claims against manufacturers and developers

Redundancy Allocation of Partitioned Linear Block Codes

Most memories suffer from both permanent defects and intermittent random errors. The partitioned linear block codes (PLBC) were proposed by Heegard to efficiently mask stuck-at defects and correct random errors. The PLBC have two separate redundancy parts for defects and random errors. In this paper, we investigate the allocation of redundancy between these two parts. The optimal redundancy allocation will be investigated using simulations and the simulation results show that the PLBC can significantly reduce the probability of decoding failure in memory with defects. In addition, we will derive the upper bound on the probability of decoding failure of PLBC and estimate the optimal redundancy allocation using this upper bound. The estimated redundancy allocation matches the optimal redundancy allocation well.Comment: 5 pages, 2 figures, to appear in IEEE International Symposium on Information Theory (ISIT), Jul. 201

The role of topologigal defects in cosmology

Topological defects are involved in a plethora of physical and astrophysical phenomena. In these lectures, I will review the r\^ ole they could play in the large-scale structure formation and the anisotropies of the cosmic microwave background, as well as in various high energy phenomena, including baryon number asymmetry, ultra-high energy cosmic rays, and gamma ray bursts. I will then summarize the gravitational effects of cosmic strings. Finally, I will briefly discuss the r\^ ole of topological defects in brane world cosmology.Comment: Invited lectures in the NATO ASI / COSLAB (ESF) School ``Patterns of symmetry breaking'', September 2002 (Cracow). 28 page

Fluid dynamics video of domains with spiral dislocations formed in the wake of an enslaved phase-separation front

Enslaved phase-separation fronts that move with a speed just smaller than that of a free front will leave in their wake a morphology of alternating domains that are roughly aligned with the front. However, these alternating domains will typically not be in phase initially. Instead there are defects. Here we present novel phase-separation morphologies that are formed in such systems where the defects are reminiscent of spiral dislocations in crystal growth.Comment: 1 pag