A Skyrme-type proposal for baryonic matter

The Skyrme model is a low-energy effective field theory for QCD, where the baryons emerge as soliton solutions. It is, however, not so easy within the standard Skyrme model to reproduce the almost exact linear growth of the nuclear masses with the baryon number (topological charge), due to the lack of Bogomolny solutions in this model, which has also hindered analytical progress. Here we identify a submodel within the Skyrme-type low energy effective action which does have a Bogomolny bound and exact Bogomolny solutions, and therefore, at least at the classical level, reproduces the nuclear masses by construction. Due to its high symmetry, this model qualitatively reproduces the main features of the liquid droplet model of nuclei. Finally, we discuss under which circumstances the proposed sextic term, which is of an essentially geometric and topological nature, can be expected to give a reasonable description of properties of nuclei.Comment: 11 pages, 2 figures, latex. v3: Extended and revised version, some clarifications added. Some references and 2 figures added. v4: matches published versio

Modelling the effects of aquatic plant growth and management on the hydraulics of a chalk stream

One of the major factors affecting flood conveyance in small to medium-sized water courses is the growth of aquatic plants. In-stream vegetation increases the resistance to flow, giving higher flood levels for a given discharge and leading to greater incidence of over-bank flooding. This thesis is focused on vegetation, characteristic of a chalk stream. Here, vegetation management is as much for the provision and maintenance of habitat as for flood risk. In order to balance these two demands, new tools are required which enable sound estimates of both flood conveyance and changes in habitat suitability. To this end, a three-dimensional hydraulic model is developed for a typical chalk stream. A novel methodology for modelling the impact of in-stream vegetation on river flow hydraulics is developed using the double-averaged Navier-Stokes equations. This is implemented within general purpose computational fluid dynamics software and tested using field measurements taken during both summer and autumn, before and after vegetation management. The model performs well when compared to field measurements of flow velocity and turbulent kinetic energy. Results show that the complex three-dimensional morphology of Ranunculus spp is shown to have a key role in energy loss and a marked impact on the distribution of flow velocities and turbulent kinetic energy. Vegetation management is discussed in terms of its effect on flow velocity, turbulent kinetic energy, flow depth, conveyance capacity and in-channel habitat. A sensitivity analysis shows the importance of rigorous data collection and guidance is provided as to which measurements have the greatest influence on calibrated model parameters. Finally, possible implications of the findings of this study for conveyance estimation methodologies and the management of aquatic vegetation are provided

Skyrmions with low binding energies

Nuclear binding energies are investigated in two variants of the Skyrme model: the first replaces the usual Skyrme term with a term that is sixth order in derivatives, and the second includes a potential that is quartic in the pion fields. Solitons in the first model are shown to deviate significantly from ansätze previously assumed in the literature. The binding energies obtained in both models are lower than those obtained from the standard Skyrme model, and those obtained in the second model are close to the experimental values

Magnetothermodynamics of BPS baby skyrmions

The magnetothermodynamics of skyrmion type matter described by the gauged BPS baby Skyrme model at zero temperature is investigated. We prove that the BPS property of the model is preserved also for boundary conditions corresponding to an asymptotically constant magnetic field. The BPS bound and the corresponding BPS equations saturating the bound are found. Further, we show that one may introduce pressure in the gauged model by a redefinition of the superpotential. Interestingly, this is related to non-extremal type solutions in the so-called fake supersymmetry method. Finally, we compute the equation of state of magnetized BSP baby skyrmions inserted into an external constant magnetic field $H$ and under external pressure $P$, i.e., $V=V(P,H)$, where $V$ is the "volume" (area) occupied by the skyrmions. We show that the BPS baby skyrmions form a ferromagnetic medium.Comment: Latex, 39 pages, 14 figures. v2: New results and references added, physical interpretation partly change

Near BPS Skyrmions and restricted harmonic maps

Motivated by a class of near BPS Skyrme models introduced by Adam, Sánchez-Guillén and Wereszczyński, the following variant of the harmonic map problem is introduced: a map φ:(M,g)→(N,h)φ:(M,g)→(N,h) between Riemannian manifolds is restricted harmonic if it locally extremizes E2E2 on its View the MathML sourceSDiff(M) orbit, where View the MathML sourceSDiff(M) denotes the group of volume preserving diffeomorphisms of (M,g)(M,g), and E2E2 denotes the Dirichlet energy. It is conjectured that near BPS skyrmions tend to restricted harmonic maps in the BPS limit. It is shown that φφ is restricted harmonic if and only if φ∗hφ∗h has exact divergence, and a linear stability theory of restricted harmonic maps is developed, from which it follows that all weakly conformal maps are stable restricted harmonic. Examples of restricted harmonic maps in every degree class R3→SU(2)R3→SU(2) and R2→S2R2→S2 are constructed. It is shown that the axially symmetric BPS skyrmions on which all previous analytic studies of near BPS Skyrme models have been based, are not restricted harmonic, casting doubt on the phenomenological predictions of such studies. The problem of minimizing E2E2 for φ:Rk→Nφ:Rk→N over all linear volume preserving diffeomorphisms is solved explicitly, and a deformed axially symmetric family of Skyrme fields constructed which are candidates for approximate near BPS skyrmions at low baryon number. The notion of restricted harmonicity is generalized to restricted FF-criticality where FF is any functional on maps (M,g)→(N,h)(M,g)→(N,h) which is, in a precise sense, geometrically natural. The case where FF is a linear combination of E2E2 and E4E4, the usual Skyrme term, is studied in detail, and it is shown that inverse stereographic projection R3→S3≡SU(2)R3→S3≡SU(2) is stable restricted FF-critical for every such FF

Topological energy bounds for the Skyrme and Faddeev models with massive pions

A topological lower bound on the Skyrme energy which depends explicitly on the pion mass is derived. This bound coincides with the previously best known bound when the pion mass vanishes, and improves on it whenever the pion mass is non-zero. The new bound can in particular circumstances be saturated. New energy bounds are also derived for the Skyrme model on a compact manifold, for the Faddeev–Skyrme model with a potential term, and for the Aratyn–Ferreira–Zimerman and Nicole models

New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.Comment: 23 page

Layer- and Direction-Specific Material Properties, Extreme Extensibility and Ultimate Material Strength of Human Abdominal Aorta and Aneurysm: A Uniaxial Extension Study.

Mechanical analysis has the potential to provide complementary information to aneurysm morphology in assessing its vulnerability. Reliable calculations require accurate material properties of individual aneurysmal components. Quantification of extreme extensibility and ultimate material strength of the tissue are important if rupture is to be modelled. Tissue pieces from 11 abdomen aortic aneurysm (AAA) from patients scheduled for elective surgery and from 8 normal aortic artery (NAA) from patients who scheduled for kidney/liver transplant were collected at surgery and banked in liquid nitrogen with the use of Cryoprotectant solution to minimize frozen damage. Prior to testing, specimen were thawed and longitudinal and circumferential tissue strips were cut from each piece and adventitia, media and thrombus if presented were isolated for the material test. The incremental Young's modulus of adventitia of NAA was direction-dependent at low stretch levels, but not the media. Both adventitia and media had a similar extreme extensibility in the circumferential direction, but the adventitia was much stronger. For aneurysmal tissues, no significant differences were found when the incremental moduli of adventitia, media or thrombus in both directions were compared. Adventitia and media from AAA had similar extreme extensibility and ultimate strength in both directions and thrombus was the weakest material. Adventitia and media from AAA were less extensible compared with those of NAA, but the ultimate strength remained similar. The material properties, including extreme extensibility and ultimate strength, of both healthy aortic and aneurysmal tissues were layer-dependent, but not direction-dependent.This research is supported by BHF PG/11/74/ 29100, HRUK RG2638/14/16, the NIHR Cambridge Biomedical Research Centre, and National Natural Science Foundation of China (81170291).This is the final version. It was first published by Springer at http://dx.doi.org/10.1007/s10439-015-1323-

A uni-extension study on the ultimate material strength and extreme extensibility of atherosclerotic tissue in human carotid plaques.

Atherosclerotic plaque rupture occurs when mechanical loading exceeds its material strength. Mechanical analysis has been shown to be complementary to the morphology and composition for assessing vulnerability. However, strength and stretch thresholds for mechanics-based assessment are currently lacking. This study aims to quantify the ultimate material strength and extreme extensibility of atherosclerotic components from human carotid plaques. Tissue strips of fibrous cap, media, lipid core and intraplaque hemorrhage/thrombus were obtained from 21 carotid endarterectomy samples of symptomatic patients. Uni-extension test with tissue strips was performed until they broke or slid. The Cauchy stress and stretch ratio at the peak loading of strips broken about 2mm away from the clamp were used to characterize their ultimate strength and extensibility. Results obtained indicated that ultimate strength of fibrous cap and media were 158.3 [72.1, 259.3] kPa (Median [Inter quartile range]) and 247.6 [169.0, 419.9] kPa, respectively; those of lipid and intraplaque hemorrhage/thrombus were 68.8 [48.5, 86.6] kPa and 83.0 [52.1, 124.9] kPa, respectively. The extensibility of each tissue type were: fibrous cap - 1.18 [1.10, 1.27]; media - 1.21 [1.17, 1.32]; lipid - 1.25 [1.11, 1.30] and intraplaque hemorrhage/thrombus - 1.20 [1.17, 1.44]. Overall, the strength of fibrous cap and media were comparable and so were lipid and intraplaque hemorrhage/thrombus. Both fibrous cap and media were significantly stronger than either lipid or intraplaque hemorrhage/thrombus. All atherosclerotic components had similar extensibility. Moreover, fibrous cap strength in the proximal region (closer to the heart) was lower than that of the distal. These results are helpful in understanding the material behavior of atherosclerotic plaques.This research is supported by BHF PG/11/74/29100, HRUK RG2638/14/16, the NIHR Cambridge Biomedical Research Centre and National Natural Science Foundation of China (81170291).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jbiomech.2015.09.03