Asymptotic Self-Similarity of Minimizers and Local Bounds in a Model of Shape-Memory Alloys

We prove that microstructures in shape-memory alloys have a self-similar refinement pattern close to austenite-martensite interfaces, working within the scalar Kohn-Müller model. The latter is based on nonlinear elasticity and includes a singular perturbation representing the energy of the interfaces between martensitic variants. Our results include the case of low-hysteresis materials in which one variant has a small volume fraction. Precisely, we prove asymptotic self-similarity in the sense of strong convergence of blow-ups around points at the austenite-martensite interface. Key ingredients in the proof are pointwise estimates and local energy bounds. This generalizes previous results by one of us to various boundary conditions, arbitrary rectangular domains, and arbitrary volume fractions of the martensitic variants, including the regime in which the energy scales as $\varepsilon ^{2/3}$ ε 2 / 3 as well as the one where the energy scales as $\varepsilon ^{1/2}$ ε 1 / 2 .

A model for gauged skyrmions with low binding energies

We consider gauged skyrmions with boundary conditions which break the gauge from SU(2) to U(1) in models derived from Yang–Mills theory. After deriving general topological energy bounds, we approximate charge 1 energy minimisers using KvBLL calorons with non-trivial asymptotic holonomy, use them to calibrate the model to optimise the ratio of energy to lower bound, and compare them with solutions to full numerical simulation. Skyrmions from calorons with non-trivial asymptotic holonomy exhibit a non-zero magnetic dipole moment, which we calculate explicitly, and compare with experimental values for the proton and the neutron. We thus propose a way to develop a physically realistic Skyrme–Maxwell theory, with the potential for exhibiting low binding energies.

On the Jordan–Moore–Gibson–Thompson Wave Equation in Hereditary Fluids with Quadratic Gradient Nonlinearity

We prove global solvability of the third-order in time Jordan–More–Gibson–Thompson acoustic wave equation with memory in $${\mathbb {R}}^n$$ R n , where $$n \ge 3$$ n ≥ 3 . This wave equation models ultrasonic propagation in relaxing hereditary fluids and incorporates both local and cumulative nonlinear effects. The proof of global existence is based on a sequence of high-order energy bounds that are uniform in time, and derived under the assumption of an exponentially decaying memory kernel and sufficiently small and regular initial data.

Global Evolution of the U(1) Higgs Boson: Nonlinear Stability and Uniform Energy Bounds

Relying on the hyperboloidal foliation method, we establish the nonlinear stability of the ground state of the U(1) standard model of electroweak interactions. This amounts to establishing a global-in-time theory for the initial value problem for a nonlinear wave–Klein–Gordon system that couples (Dirac, scalar, gauge) massive equations together. In particular, we investigate here the Dirac equation and study a new energy functional defined with respect to the hyperboloidal foliation of Minkowski spacetime. We provide a decay result for the Dirac equation which is uniform in the mass coefficient and thus allows for the Dirac mass coefficient to be arbitrarily small. Furthermore, we establish energy bounds for the Higgs fields and gauge bosons that are uniform with respect to the hyperboloidal time variable.

The persistence of the Chekanov–Eliashberg algebra

We apply the barcodes of persistent homology theory to the c Chekanov–Eliashberg algebra of a Legendrian submanifold to deduce displacement energy bounds for arbitrary Legendrians. We do not require the full Chekanov–Eliashberg algebra to admit an augmentation as we linearize the algebra only below a certain action level. As an application we show that it is not possible to $$C^0$$ C 0 -approximate a stabilized Legendrian by a Legendrian that admits an augmentation.

Polynomial energy bounds for type F4 WZW-models

We prove that for any type [Formula: see text] unitary affine VOA [Formula: see text], sufficiently many intertwining operators satisfy polynomial energy bounds. This finishes the Wassermann type analysis of intertwining operators for all WZW-models.

On convergence of approximate solutions to the compressible Euler system

We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence either (i) converges strongly in the energy norm, or (ii) the limit is not a weak solution of the associated Euler system. This is in sharp contrast to the incompressible case, where (oscillatory) approximate solutions may converge weakly to solutions of the Euler system. Our approach leans on identifying a system of differential equations satisfied by the associated turbulent defect measure and showing that it only has a trivial solution.

Static wormhole solutions and Noether symmetry in modified Gauss–Bonnet gravity

In this paper, we analyze static traversable wormholes via Noether symmetry technique in modified Gauss–Bonnet $$f(\mathcal {G})$$f(G) theory of gravity (where $$\mathcal {G}$$G represents Gauss–Bonnet term). We assume isotropic matter configuration and spherically symmetric metric. We construct three $$f(\mathcal {G})$$f(G) models, i.e, linear, quadratic and exponential forms and examine the consistency of these models. The traversable nature of wormhole solutions is discussed via null energy bound of the effective stress–energy tensor while physical behavior is studied through standard energy bounds of isotropic fluid. We also discuss the stability of these wormholes inside the wormhole throat and conclude the presence of traversable and physically stable wormholes for quadratic as well as exponential $$f(\mathcal {G})$$f(G) models.