Sphalerons, spectral flow, and anomalies

The topology of configuration space may be responsible in part for the existence of sphalerons. Here, sphalerons are defined to be static but unstable finite-energy solutions of the classical field equations. Another manifestation of the nontrivial topology of configuration space is the phenomenon of spectral flow for the eigenvalues of the Dirac Hamiltonian. The spectral flow, in turn, is related to the possible existence of anomalies. In this review, the interconnection of these topics is illustrated for three particular sphalerons of SU(2) Yang-Mills-Higgs theory.Comment: 35 pages with revtex4; invited paper for the August special issue of JMP on "Integrability, topological solitons and beyond

Wear of human teeth: a tribological perspective

The four main types of wear in teeth are attrition (enamel-on-enamel contact), abrasion (wear due to abrasive particles in food or toothpaste), abfraction (cracking in enamel and subsequent material loss), and erosion (chemical decomposition of the tooth). They occur as a result of a number of mechanisms including thegosis (sliding of teeth into their lateral position), bruxism (tooth grinding), mastication (chewing), toothbrushing, tooth flexure, and chemical effects. In this paper the current understanding of wear of enamel and dentine in teeth is reviewed in terms of these mechanisms and the major influencing factors are examined. In vitro tooth wear simulation and in vivo wear measurement and ranking are also discussed

Level Crossing Along Sphaleron Barriers

In the electroweak sector of the standard model topologically inequivalent vacua are separated by finite energy barriers, whose height is given by the sphale\-ron. For large values of the Higgs mass there exist several sphaleron solutions and the barriers are no longer symmetric. We construct paths of classical configurations from one vacuum to a neighbouring one and solve the fermion equations in the background field configurations along such paths, choosing the fermions of a doublet degenerate in mass. As in the case of light Higgs masses we observe the level crossing phenomenon also for large Higgs masses.Comment: 17 pages, latex, 10 figures in uuencoded postscript files. THU-94/0

The Sphaleron Barrier in the Presence of Fermions

We calculate the minimal energy path over the sphaleron barrier in the pre\-sen\-ce of fermions, assuming that the fermions of a doublet are degenerate in mass. This allows for spherically symmetric ans\"atze for the fields, when the mixing angle dependence is neglected. While light fermions have little influence on the barrier, the presence of heavy fermions ($M_F \sim$ TeV) strongly deforms the barrier, giving rise to additional sphalerons for very heavy fermions ($M_F \sim$ 10 TeV). Heavy fermions form non-topological solitons in the vacuum sector.Comment: 19 pages, latex, 18 figures in 3 seperate uuencoded postscript files THU-93/1

Insights into surface chemistry down to nanoscale: an accessible colour hyperspectral imaging approach for scanning electron microscopy

Chemical imaging (CI) is the spatial identification of molecular chemical composition and is critical to characterising the (in-) homogeneity of functional material surfaces. Nanoscale CI on bulk functional material surfaces is a longstanding challenge in materials science and is addressed here. We demonstrate the feasibility of surface sensitive CI in the scanning electron microscope (SEM) using colour enriched secondary electron hyperspectral imaging (CSEHI). CSEHI is a new concept in the SEM, where secondary electron emissions in up to three energy ranges are assigned to RGB (red, green, blue) image colour channels. The energy ranges are applied to a hyperspectral image volume which is collected in as little as 50 s. The energy ranges can be defined manually or automatically. Manual application requires additional information from the user as first explained and demonstrated for a lithium metal anode (LMA) material, followed by manual CSEHI for a range of materials from art history to zoology. We introduce automated CSEHI, eliminating the need for additional user information, by finding energy ranges using a non-negative matrix factorization (NNMF) based method. Automated CSEHI is evaluated threefold: (1) benchmarking to manual CSEHI on LMA; (2) tracking controlled changes to LMA surfaces; (3) comparing automated CSEHI and manual CI results published in the past to reveal nanostructures in peacock feather and spider silk. Based on the evaluation, CSEHI is well placed to differentiate/track several lithium compounds formed through a solution reaction mechanism on a LMA surface (eg. lithium carbonate, lithium hydroxide and lithium nitride). CSEHI was used to provide insights into the surface chemical distribution on the surface of samples from art history (mineral phases) to zoology (di-sulphide bridge localisation) that are hidden from existing surface analysis techniques. Hence, the CSEHI approach has the potential to impact the way materials are analysed for scientific and industrial purposes

Nondegenerate Fermions in the Background of the Sphaleron Barrier

We consider level crossing in the background of the sphaleron barrier for nondegenerate fermions. The mass splitting within the fermion doublets allows only for an axially symmetric ansatz for the fermion fields. In the background of the sphaleron we solve the partial differential equations for the fermion functions. We find little angular dependence for our choice of ansatz. We therefore propose a good approximate ansatz with radial functions only. We generalize this approximate ansatz with radial functions only to fermions in the background of the sphaleron barrier and argue, that it is a good approximation there, too.Comment: LATEX, 20 pages, 11 figure

Insights into surface chemistry down to nanoscale: an accessible colour hyperspectral imaging approach for scanning electron microscopy

Chemical imaging (CI) is the spatial identification of molecular chemical composition and is critical to characterising the (in-) homogeneity of functional material surfaces. Nanoscale CI on bulk functional material surfaces is a longstanding challenge in materials science and is addressed here. We demonstrate the feasibility of surface sensitive CI in the scanning electron microscope (SEM) using colour enriched secondary electron hyperspectral imaging (CSEHI). CSEHI is a new concept in the SEM, where secondary electron emissions in up to three energy ranges are assigned to RGB (red, green, blue) image colour channels. The energy ranges are applied to a hyperspectral image volume which is collected in as little as 50 s. The energy ranges can be defined manually or automatically. Manual application requires additional information from the user as first explained and demonstrated for a lithium metal anode (LMA) material, followed by manual CSEHI for a range of materials from art history to zoology. We introduce automated CSEHI, eliminating the need for additional user information, by finding energy ranges using a non-negative matrix factorization (NNMF) based method. Automated CSEHI is evaluated threefold: (1) benchmarking to manual CSEHI on LMA; (2) tracking controlled changes to LMA surfaces; (3) comparing automated CSEHI and manual CI results published in the past to reveal nanostructures in peacock feather and spider silk. Based on the evaluation, CSEHI is well placed to differentiate/track several lithium compounds formed through a solution reaction mechanism on a LMA surface (eg. lithium carbonate, lithium hydroxide and lithium nitride). CSEHI was used to provide insights into the surface chemical distribution on the surface of samples from art history (mineral phases) to zoology (di-sulphide bridge localisation) that are hidden from existing surface analysis techniques. Hence, the CSEHI approach has the potential to impact the way materials are analysed for scientific and industrial purposes

Gradient Approach to the Sphaleron Barrier

We apply the gradient approach to obtain a path over the sphaleron barrier and to demonstrate the fermionic level crossing phenomenon. Neglecting the mixing angle dependence and assuming that the fermions of a doublet are degenerate in mass we employ spherically symmetric ans\"atze for the fields. The gradient path over the barrier is smooth, even for large values of the Higgs boson mass or of the fermion mass, where the extremal energy path bifurcates.Comment: 20 pages, latex, 13 figures in uuencoded postscript files. THU-94/1

Spectral flow of chiral fermions in nondissipative Yang-Mills gauge field backgrounds

Real-time anomalous fermion number violation is investigated for massless chiral fermions in spherically symmetric SU(2) Yang-Mills gauge field backgrounds which can be weakly dissipative or even nondissipative. Restricting consideration to spherically symmetric fermion fields, the zero-eigenvalue equation of the time-dependent effective Dirac Hamiltonian is studied in detail. For generic spherically symmetric SU(2) gauge fields in Minkowski spacetime, a relation is presented between the spectral flow and two characteristics of the background gauge field. These characteristics are the well-known ``winding factor,'' which is defined to be the change of the Chern-Simons number of the associated vacuum sector of the background gauge field, and a new ``twist factor,'' which can be obtained from the zero-eigenvalue equation of the effective Dirac Hamiltonian but is entirely determined by the background gauge field. For a particular class of (weakly dissipative) Luscher-Schechter gauge field solutions, the level crossings are calculated directly and nontrivial contributions to the spectral flow from both the winding factor and the twist factor are observed. The general result for the spectral flow may be relevant to electroweak baryon number violation in the early universe.Comment: REVTeX, 43 pages, v4: final versio

Characterisation and Skin Distribution of Lecithin-Based Coenzyme Q10-Loaded Lipid Nanocapsules

The purpose of this study was to investigate the influence of the inner lipid ratio on the physicochemical properties and skin targeting of surfactant-free lecithin-based coenzyme Q10-loaded lipid nanocapsules (CoQ10-LNCs). The smaller particle size of CoQ10-LNCs was achieved by high pressure and a lower ratio of CoQ10/GTCC (Caprylic/capric triglyceride); however, the zeta potential of CoQ10-LNCs was above /− 60 mV/ with no distinct difference among them at different ratios of CoQ10/GTCC. Both the crystallisation point and the index decreased with the decreasing ratio of CoQ10/GTCC and smaller particle size; interestingly, the supercooled state of CoQ10-LNCs was observed at particle size below about 200 nm, as verified by differential scanning calorimetry (DSC) in one heating–cooling cycle. The lecithin monolayer sphere structure of CoQ10-LNCs was investigated by cryogenic transmission electron microscopy (Cryo-TEM). The skin penetration results revealed that the distribution of Nile red-loaded CoQ10-LNCs depended on the ratio of inner CoQ10/GTCC; moreover, epidermal targeting and superficial dermal targeting were achieved by the CoQ10-LNCs application. The highest fluorescence response was observed at a ratio of inner CoQ10/GTCC of 1:1. These observations suggest that lecithin-based LNCs could be used as a promising topical delivery vehicle for lipophilic compounds