All Outputs (199)

Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’ (2021)
Journal Article
Krause, A. L., Gaffney, E. A., Maini, P. K., & Klika, V. (2021). Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379(2213), https://doi.org/10.1098/rsta.2020.0280

Elucidating pattern forming processes is an important problem in the physical, chemical and biological sciences. Turing’s contribution, after being initially neglected, eventually catalysed a huge amount of work from mathematicians, physicists, chemi... Read More about Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

Modern perspectives on near-equilibrium analysis of Turing systems (2021)
Journal Article
Krause, A. L., Gaffney, E. A., Maini, P. K., & Klika, V. (2021). Modern perspectives on near-equilibrium analysis of Turing systems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379(2213), Article 20200268. https://doi.org/10.1098/rsta.2020.0268

In the nearly seven decades since the publication of Alan Turing’s work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction–diffusion theory. Some of these developme... Read More about Modern perspectives on near-equilibrium analysis of Turing systems.

A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$ (2021)
Journal Article
Vishe, P. (2022). A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$. Transactions of the American Mathematical Society, 375(1), 669-694. https://doi.org/10.1090/tran/8498

Let G = SL(2, R) n, let Γ = Γn 0 , where Γ0 is a co-compact lattice in SL(2, R), let F(x) be a non-singular quadratic form and let u(x1, ..., xn) := 1 x1 0 1 ×...× 1 xn 0 1 denote unipotent elements in G which generate an n dimensional horospherical... Read More about A sparse equidistribution result for $(\mathrm{SL}(2,\mathbb{R})/\Gamma_0)^{n}$.

Intrinsic winding of braided vector fields in tubular subdomains (2021)
Journal Article
Prior, C. B., & Yeates, A. R. (2021). Intrinsic winding of braided vector fields in tubular subdomains. Journal of Physics A: Mathematical and Theoretical, 54(46), Article 465701. https://doi.org/10.1088/1751-8121/ac2ea3

Braided vector fields on spatial subdomains which are homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the v... Read More about Intrinsic winding of braided vector fields in tubular subdomains.

Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces (2021)
Journal Article
Feng, C., & Li, L. (2022). Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces. Advances in operator theory, 7, Article 5. https://doi.org/10.1007/s43036-021-00170-1

Saint Raymond asked whether continuously differentiable maps with isolated critical points are necessarily open in infinite dimensional (Hilbert) spaces. We answer this question negatively by constructing counterexamples in various settings including... Read More about Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces.

Efficiency of delayed-acceptance random walk Metropolis algorithms (2021)
Journal Article
Sherlock, C., Thiery, A. H., & Golightly, A. (2021). Efficiency of delayed-acceptance random walk Metropolis algorithms. Annals of Statistics, 49(5), 2972-2990. https://doi.org/10.1214/21-aos2068

Delayed-acceptance Metropolis–Hastings and delayed-acceptance pseudo-marginal Metropolis–Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation thereof, but a co... Read More about Efficiency of delayed-acceptance random walk Metropolis algorithms.

Multiparticle Solutions to Einstein’s Equations (2021)
Journal Article
Gomez, H., & Lipinski Jusinskas, R. (2021). Multiparticle Solutions to Einstein’s Equations. Physical Review Letters, 127(18), Article 181603. https://doi.org/10.1103/physrevlett.127.181603

In this Letter, we present the first multiparticle solutions to Einstein’s field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity’s infinite number of vertices with... Read More about Multiparticle Solutions to Einstein’s Equations.

Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement (2021)
Journal Article
Midgley, L., Bourhis, L. J., Dolomanov, O. V., Grabowsky, S., Kleemiss, F., Puschmann, H., & Peyerimhoff, N. (2021). Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement. Acta Crystallographica Section A: Foundations and Advances, 77(6), 519-533. https://doi.org/10.1107/s2053273321009086

When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-sph... Read More about Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement.

Correlations in totally symmetric self-complementary plane partitions (2021)
Journal Article
Ayyer, A., & Chhita, S. (2021). Correlations in totally symmetric self-complementary plane partitions. Transactions of the London Mathematical Society, 8(1), 493-526. https://doi.org/10.1112/tlm3.12039

Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in one-twelfth of a hexagon... Read More about Correlations in totally symmetric self-complementary plane partitions.

Squarefree Integers in Arithmetic Progressions to Smooth Moduli (2021)
Journal Article
Mangerel, A. P. (2021). Squarefree Integers in Arithmetic Progressions to Smooth Moduli. Forum of Mathematics, Sigma, 9, Article e72. https://doi.org/10.1017/fms.2021.67

Let ε>0 be sufficiently small and let 0

Is flare-ribbon fine structure related to tearing in the flare current sheet? (2021)
Journal Article
Wyper, P., & Pontin, D. (2021). Is flare-ribbon fine structure related to tearing in the flare current sheet?. Astrophysical Journal, 920(2), Article 102. https://doi.org/10.3847/1538-4357/ac1943

Observations of solar flare ribbons show significant fine structure in the form of breaking wave-like perturbations and spirals. The origin of this structure is not well understood, but one possibility is that it is related to the tearing instability... Read More about Is flare-ribbon fine structure related to tearing in the flare current sheet?.

Embedding spheres in knot traces (2021)
Journal Article
Feller, P., Miller, A. N., Nagel, M., Orson, P., Powell, M., & Ray, A. (2021). Embedding spheres in knot traces. Compositio Mathematica, 157(10), 2242-2279. https://doi.org/10.1112/s0010437x21007508

The trace of the n-framed surgery on a knot in S3 is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded 2-sphere whose compleme... Read More about Embedding spheres in knot traces.

On the consistency of (partially-)massless matter couplings in de Sitter space (2021)
Journal Article
Sleight, C., & Taronna, M. (2021). On the consistency of (partially-)massless matter couplings in de Sitter space. Journal of High Energy Physics, 2021(10), Article 156 (2021). https://doi.org/10.1007/jhep10%282021%29156

We study the consistency of the cubic couplings of a (partially-)massless spinning field to two scalars in (d + 1)-dimensional de Sitter space. Gauge invariance of observables with external (partially)-massless spinning fields translates into Ward-Ta... Read More about On the consistency of (partially-)massless matter couplings in de Sitter space.

Survival signature for reliability evaluation of a multi-state system with multi-state components (2021)
Journal Article
Qin, J., & Coolen, F. (2022). Survival signature for reliability evaluation of a multi-state system with multi-state components. Reliability Engineering & System Safety, 218(Part A), Article 108129. https://doi.org/10.1016/j.ress.2021.108129

Survival signature technology has recently attracted increasing attention for its merits on quantifying reliability of systems with multiple types of components. In order to implement reliability evaluation of multi-state system (MSS), computing meth... Read More about Survival signature for reliability evaluation of a multi-state system with multi-state components.

Evolving to Non-round Weingarten Spheres: Integer Linear Hopf Flows (2021)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2021). Evolving to Non-round Weingarten Spheres: Integer Linear Hopf Flows. Partial Differential Equations and Applications, 2(6), Article 72. https://doi.org/10.1007/s42985-021-00128-1

In the 1950’s Hopf gave examples of non-round convex 2-spheres in Euclidean 3-space with rotational symmetry that satisfy a linear relationship between their principal curvatures. In this paper, we investigate conditions under which evolving a smooth... Read More about Evolving to Non-round Weingarten Spheres: Integer Linear Hopf Flows.

Ergodicity of Sublinear Markovian Semigroups (2021)
Journal Article
Feng, C., & Zhao, H. (2021). Ergodicity of Sublinear Markovian Semigroups. SIAM Journal on Mathematical Analysis, 53(5), 5646-5681. https://doi.org/10.1137/20m1356518

In this paper, we study the ergodicity of invariant sublinear expectation of sublinear Markovian semigroup. For this, we first develop an ergodic theory of an expectation-preserving map on a sublinear expectation space. Ergodicity is defined as any i... Read More about Ergodicity of Sublinear Markovian Semigroups.

Magnetic quivers from brane webs with O7+-planes (2021)
Journal Article
Akhond, M., & Carta, F. (2021). Magnetic quivers from brane webs with O7+-planes. Journal of High Energy Physics, 2021(10), https://doi.org/10.1007/jhep10%282021%29014

We consider the Higgs branch of 5d fixed points engineered using brane webs with an O7+-plane. We use the brane construction to propose a set of rules to extract the corresponding magnetic quivers. Such magnetic quivers are generically framed non-sim... Read More about Magnetic quivers from brane webs with O7+-planes.

The rectangular peg problem (2021)
Journal Article
Greene, J., & Lobb, A. (2021). The rectangular peg problem. Annals of Mathematics, 194(2), 509-517. https://doi.org/10.4007/annals.2021.194.2.4

For every smooth Jordan curve and rectangle R in the Euclidean plane, we show that there exists a rectangle similar to R whose vertices lie on . The proof relies on the theorem of Shevchishin and Nemirovski that the Klein bottle does not admit a smoo... Read More about The rectangular peg problem.

On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators (2021)
Journal Article
Boegli, S., & Stampach, F. (2021). On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators. Journal of Spectral Theory, 11(3), 1391-1413. https://doi.org/10.4171/jst/378

We study to what extent Lieb–Thirring inequalities are extendable from self-adjoint to general (possibly non-self-adjoint) Jacobi and Schrödinger operators. Namely, we prove the conjecture of Hansmann and Katriel from [12] and answer another open que... Read More about On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators.

Non-invertible global symmetries and completeness of the spectrum (2021)
Journal Article
Heidenreich, B., McNamara, J., Montero, M., Reece, M., Rudelius, T., & Valenzuela, I. (2021). Non-invertible global symmetries and completeness of the spectrum. Journal of High Energy Physics, 2021(9), Article 203. https://doi.org/10.1007/jhep09%282021%29203

It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness... Read More about Non-invertible global symmetries and completeness of the spectrum.