Skyrmion and Baby Skyrmion Formation from Domain Walls

We numerically simulate the formation of $(2+1)$-dimensional baby Skyrmions and $(3+1)$-dimensional $SU(2)$ Skyrmions from domain wall collisions. It has been suggested that Skyrmion, anti-Skyrmion pairs can be produced from the interaction of two domain walls. This is confirmed, however it is also demonstrated that the process can require quite precise conditions. An alternative, more stable, formation process is proposed as the interaction of more than two segments of domain wall. This is simulated, requiring far less constraints on the initial conditions used. Finally domain wall networks are considered, demonstrating how Skyrmions may be produced in a complex dynamical system. We show that the local topological charge configurations, formed within the system, are countered by opposite winding on the boundary of the system to conserve topological charge.Comment: 14 page

Hyperbolic Skyrmions

We investigate SU(2) Skyrmions in hyperbolic space, by computing numerical solutions of the nonlinear field equation. We first demonstrate the link between increasing curvature and the accuracy of the rational map approximation to the minimal energy static solutions. We investigate the link between Skyrmions with massive pions in Euclidean space and the massless case in hyperbolic space, by relating curvature to the pion mass. Crystal chunks are found to be the minimal energy solution for increased curvature as well as increased mass of the model. The dynamics of the hyperbolic model are also simulated, with the similarities and differences to the Euclidean model noted

The Skyrme Model: Curved Space, Symmetries and Mass

The presented thesis contains research on topological solitons in (2+1) and (3+1) dimensional classical field theories, focusing upon the Skyrme model. Due to the highly non-linear nature of this model, we must consider various numerical methods to find solutions. We initially consider the (2+1) baby Skyrme model, demonstrating that the currently accepted form of minimal energy solutions, namely straight chains of alternating phase solitons, does not hold for higher charge. Ring solutions with relative phases changing by pi for even configurations or pi-pi/B for odd numbered configurations, are demonstrated to have lower energy than the traditional chain configurations above a certain charge threshold, which is dependant on the parameters of the model. Crystal chunk solutions are then demonstrated to take a lower energy but for extremely high values of charge. We also demonstrate the infinite charge limit of each of the above configurations. Finally, a further possibility of finding lower energy solutions is discussed in the form of soliton networks involving rings/chains and junctions. The dynamics of some of these higher charge solutions are also considered. In chapter 3 we numerically simulate the formation of (2+1)-dimensional baby Skyrmions from domain wall collisions. It is demonstrated that Skyrmion, anti-Skyrmion pairs can be produced from the interaction of two domain walls, however the process can require quite precise conditions. An alternative, more stable, formation process is proposed and simulated as the interaction of more than two segments of domain wall. Finally domain wall networks are considered, demonstrating how Skyrmions may be produced in a complex dynamical system. The broken planar Skyrme model, presented in chapter 4, is a theory that breaks global O(3) symmetry to the dihedral group D_N. This gives a single soliton solution formed of N constituent parts, named partons, that are topologically confined. We show that the configuration of the local energy solutions take the form of polyform structures (planar figures formed by regular N-gons joined along their edges, of which polyiamonds are the N=3 subset). Furthermore, we numerically simulate the dynamics of this model. We then consider the (3+1) SU(2) Skyrme model, introducing the familiar concepts of the model in chapter 5 and then numerically simulating their formation from domain walls. In analogue with the planar case, it is demonstrated that the process can require quite precise conditions and an alternative, more stable, formation process can be achieved with more domain walls, requiring far less constraints on the initial conditions used. The results in chapter 7 discuss the extension of the broken baby Skyrme model to the 3-dimensional SU(2) case. We first consider the affect of breaking the isospin symmetry by altering the tree level mass of one of the pion fields breaking the SO(3) isospin symmetry to an SO(2) symmetry. This serves to exemplify the constituent make up of the Skyrme model from ring like solutions. These rings then link together to form higher charge solutions. Finally the mass term is altered to allow all the fields to have an equivalent tree level mass, but the symmetry of the Lagrangian to be broken, firstly to a dihedral symmetry D_N and then to some polyhedral symmetries. We now move on to discussing both the baby and full SU(2) Skyrme models in curved spaces. In chapter 8 we investigate SU(2) Skyrmions in hyperbolic space. We first demonstrate the link between increasing curvature and the accuracy of the rational map approximation to the minimal energy static solutions. We investigate the link between Skyrmions with massive pions in Euclidean space and the massless case in hyperbolic space, by relating curvature to the pion mass. Crystal chunks are found to be the minimal energy solution for increased curvature as well as increased mass of the model. The dynamics of the hyperbolic model are also simulated, with the similarities and differences to the Euclidean model noted. One of the difficulties of studying the full Skyrme model in (3+1) dimensions is a possible crystal lattice. We hence reduce the dimension of the model and first consider crystal lattices in (2+1)-dimensions. In chapter 9 we first show that the minimal energy solutions take the same form as those from the flat space model. We then present a method of tessellating the Poincare disc model of hyperbolic space with a fundamental cell. The affect this may have on a resulting Skyrme crystal is then discussed and likely problems in simulating this process. We then consider the affects of a pure AdS background on the Skyrme model, starting with the massless baby Skyrme model in chapter 10. The asymptotics and scale of charge 1 massless radial solutions are demonstrated to take a similar form to those of the massive flat space model, with the AdS curvature playing a similar role to the flat space pion mass. Higher charge solutions are then demonstrated to exhibit a concentric ring-like structure, along with transitions (dubbed popcorn transitions in analogy with models of holographic QCD) between different numbers of layers. The 1st popcorn transitions from an n layer to an n+1-layer configuration are observed at topological charges 9 and 27 and further popcorn transitions for higher charges are predicted. Finally, a point-particle approximation for the model is derived and used to successfully predict the ring structures and popcorn transitions for higher charge solitons. The final chapter considers extending the results from the penultimate chapter to the full SU(2) model in a pure AdS_4 background. We make the prediction that the multi-layered concentric ring solutions for the 2-dimensional case would correlate a multi-layered concentric rational map configuration for the 3-dimensional model. The rational map approximation is extended to consider multi-layered maps and the energies demonstrated to reduce the minimal energy solution for charge B=11 which is again dubbed a popcorn transition. Finally we demonstrate that the multi shell structure extends to the full field solutions which are found numerically. We also discuss the affect of combined symmetries on the results which (while likely to be important) appear to be secondary to the dominant effective potential of the metric which simulates a packing problem and hence forces the popcorn transitions to act accordingly with the 2-dimensional model

Baby Skyrmions in AdS

We study the baby Skyrme model in a pure AdS background without a mass term. The tail decays and scalings of massless radial solutions are demonstrated to take a similar form to those of the massive flat space model, with the AdS curvature playing a similar role to the flat space pion mass. We also numerically find minimal energy solutions for a range of higher topological charges and find that they form concentric ring-like solutions. Popcorn transitions (named in analogy with studies of toy models of holographic QCD) from an n layer to an n + 1-layer configuration are observed at topological charges 9 and 27 and further popcorn transitions for higher charges are predicted. Finally, a pointparticle approximation for the model is derived and used to successfully predict the ring structures and popcorn transitions for higher charge solitons

Chiral p-wave superconductors have complex coherence and magnetic field penetration lengths

We show that in superconductors that break time-reversal symmetry and have anisotropy, such as p+ip materials, all order parameters and magnetic modes are mixed. Excitation of the gap fields produces an excitation of the magnetic field and vice versa. Correspondingly, the long-range decay of the magnetic field and order parameter is in general given by the same exponent. Thus, one cannot characterize p+ip superconductors by the usual coherence and magnetic field penetration lengths. Instead, the system has normal modes that are associated with linear combinations of magnetic fields, moduli of and phases of the order-parameter components. Each such normal mode has its own decay length that plays the role of a hybridized coherence/magnetic field penetration length. On a large part of the parameter space, these exponents are complex. Therefore, the system in general has damped oscillatory decay of the magnetic field accompanied by damped oscillatory variation of the order-parameter fields

Dietary nitrate reduces muscle metabolic perturbation and improves exercise tolerance in hypoxia

The definitive version is available at www3.interscience.wiley.comExercise in hypoxia is associated with reduced muscle oxidative function and impaired exercise tolerance. We hypothesised that dietary nitrate supplementation (which increases plasma [nitrite] and thus NO bioavailability) would ameliorate the adverse effects of hypoxia on muscle metabolism and oxidative function. In a double-blind, randomised crossover study, nine healthy subjects completed knee-extension exercise to the limit of tolerance (T(lim)), once in normoxia (20.9% O(2); CON) and twice in hypoxia (14.5% O(2)). During 24 h prior to the hypoxia trials, subjects consumed 0.75 L of nitrate-rich beetroot juice (9.3 mmol nitrate; H-BR) or 0.75 L of nitrate-depleted beetroot juice as a placebo (0.006 mmol nitrate; H-PL). Muscle metabolism was assessed using calibrated (31)P-MRS. Plasma [nitrite] was elevated (P < 0.01) following BR (194 ± 51 nm) compared to PL (129 ± 23 nm) and CON (142 ± 37 nM). T(lim) was reduced in H-PL compared to CON (393 ± 169 vs. 471 ± 200 s; P < 0.05) but was not different between CON and H-BR (477 ± 200 s). The muscle [PCr], [P(i)] and pH changed at a faster rate in H-PL compared to CON and H-BR. The [PCr] recovery time constant was greater (P < 0.01) in H-PL (29 ± 5 s) compared to CON (23 ± 5 s) and H-BR (24 ± 5 s). Nitrate supplementation reduced muscle metabolic perturbation during exercise in hypoxia and restored exercise tolerance and oxidative function to values observed in normoxia. The results suggest that augmenting the nitrate-nitrite-NO pathway may have important therapeutic applications for improving muscle energetics and functional capacity in hypoxia

Effects of rare kidney diseases on kidney failure: a longitudinal analysis of the UK National Registry of Rare Kidney Diseases (RaDaR) cohort

\ua9 2024 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 licenseBackground: Individuals with rare kidney diseases account for 5–10% of people with chronic kidney disease, but constitute more than 25% of patients receiving kidney replacement therapy. The National Registry of Rare Kidney Diseases (RaDaR) gathers longitudinal data from patients with these conditions, which we used to study disease progression and outcomes of death and kidney failure. Methods: People aged 0–96 years living with 28 types of rare kidney diseases were recruited from 108 UK renal care facilities. The primary outcomes were cumulative incidence of mortality and kidney failure in individuals with rare kidney diseases, which were calculated and compared with that of unselected patients with chronic kidney disease. Cumulative incidence and Kaplan–Meier survival estimates were calculated for the following outcomes: median age at kidney failure; median age at death; time from start of dialysis to death; and time from diagnosis to estimated glomerular filtration rate (eGFR) thresholds, allowing calculation of time from last eGFR of 75 mL/min per 1\ub773 m2 or more to first eGFR of less than 30 mL/min per 1\ub773 m2 (the therapeutic trial window). Findings: Between Jan 18, 2010, and July 25, 2022, 27 285 participants were recruited to RaDaR. Median follow-up time from diagnosis was 9\ub76 years (IQR 5\ub79–16\ub77). RaDaR participants had significantly higher 5-year cumulative incidence of kidney failure than 2\ub781 million UK patients with all-cause chronic kidney disease (28% vs 1%; p&lt;0\ub70001), but better survival rates (standardised mortality ratio 0\ub742 [95% CI 0\ub732–0\ub752]; p&lt;0\ub70001). Median age at kidney failure, median age at death, time from start of dialysis to death, time from diagnosis to eGFR thresholds, and therapeutic trial window all varied substantially between rare diseases. Interpretation: Patients with rare kidney diseases differ from the general population of individuals with chronic kidney disease: they have higher 5-year rates of kidney failure but higher survival than other patients with chronic kidney disease stages 3–5, and so are over-represented in the cohort of patients requiring kidney replacement therapy. Addressing unmet therapeutic need for patients with rare kidney diseases could have a large beneficial effect on long-term kidney replacement therapy demand. Funding: RaDaR is funded by the Medical Research Council, Kidney Research UK, Kidney Care UK, and the Polycystic Kidney Disease Charity

European contribution to the study of ROS: A summary of the findings and prospects for the future from the COST action BM1203 (EU-ROS).

The European Cooperation in Science and Technology (COST) provides an ideal framework to establish multi-disciplinary research networks. COST Action BM1203 (EU-ROS) represents a consortium of researchers from different disciplines who are dedicated to providing new insights and tools for better understanding redox biology and medicine and, in the long run, to finding new therapeutic strategies to target dysregulated redox processes in various diseases. This report highlights the major achievements of EU-ROS as well as research updates and new perspectives arising from its members. The EU-ROS consortium comprised more than 140 active members who worked together for four years on the topics briefly described below. The formation of reactive oxygen and nitrogen species (RONS) is an established hallmark of our aerobic environment and metabolism but RONS also act as messengers via redox regulation of essential cellular processes. The fact that many diseases have been found to be associated with oxidative stress established the theory of oxidative stress as a trigger of diseases that can be corrected by antioxidant therapy. However, while experimental studies support this thesis, clinical studies still generate controversial results, due to complex pathophysiology of oxidative stress in humans. For future improvement of antioxidant therapy and better understanding of redox-associated disease progression detailed knowledge on the sources and targets of RONS formation and discrimination of their detrimental or beneficial roles is required. In order to advance this important area of biology and medicine, highly synergistic approaches combining a variety of diverse and contrasting disciplines are needed.The EU-ROS consortium (COST Action BM1203) was supported by the European Cooperation in Science and Technology (COST). The present overview represents the final Action dissemination summarizing the major achievements of COST Action BM1203 (EU-ROS) as well as research news and personal views of its members. Some authors were also supported by COST Actions BM1005 (ENOG) and BM1307 (PROTEOSTASIS), as well as funding from the European Commission FP7 and H2020 programmes, and several national funding agencies