Research works

On the continuity of solutions to the anisotropic N-Laplacian with $$L^1$$ lower order term

Abstract We establish the continuity of bounded solutions to the anisotropic elliptic equation $$\begin{aligned} -\sum \limits _{i=1}^N\Big (|u_{x_i}|^{p_i-2} u_{x_i}\Big )_{x_i}=f(x),\quad x\in \Omega ,\quad f(x)\in L^1(\Omega ) \end{aligned}$$ under the conditions $$\begin{alig...

Multirate Runge–Kutta for Nonlinearly Partitioned Systems

Abstract. Multirate integration is an increasingly relevant tool that enables scientists to simulate multiphysics systems. Existing multirate methods are designed for equations whose fast and slow variables can be linearly separated using additive or componentwise partitions. How...

Antiferromagnetism and tightly bound Cooper pairs induced by kinetic frustration

Antiferromagnetism and superconductivity are often viewed as competing orders in correlated electron systems. Here, we demonstrate that kinetic frustration in hole motion facilitates their coexistence within the square-lattice repulsive Hubbard model. Combining exact analytical s...

The field equations of penalized non-parametric regression

Abstract We view penalized risks through the lens of the calculus of variations. We consider risks comprised of a fitness-term (e.g. MSE) and a gradient-based penalty and search for the minima of such risks. After establishing the Euler-Lagrange field equations as a systematic ap...

Improved Existence Time for the Whitham Equation and a Whitham–Boussinesq System

Abstract. In this paper, we investigate the time of existence of the solutions to two full dispersion models derived from the water waves equations in the shallow water regime: the Whitham equation and a Whitham–Boussinesq system in dimensions one and two. The regime is character...

Trade Reform in Services: Structural Change and Production Networks

ABSTRACT We study the effects of services trade reforms in a multi‐country multi‐sector quantitative trade model with input–output linkages. Services matter both as final consumption and as production inputs: cheaper traded services lower household prices directly and reduce the...

Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games

Abstract We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite-difference discretization and solve the resulting fin...

Gradient Estimates for the Insulated Conductivity Problem with Partially Flat Inclusions

Abstract. We study the insulated conductivity problem with inclusions embedded in a bounded domain in [Formula: see text]. It was known that in the setting of strictly convex inclusions, the gradient of solutions may blow up as the distance between inclusions approaches 0. The op...

Cobamide-based interactions between soil bacteria can be predicted based on monoculture growth

ABSTRACT Interactions between microbes shape the structure and function of microbial communities. While studying interactions is key to understanding microbial communities as a whole, gaining a detailed mechanistic view is challenging due to the number of co-occurring interaction...

MONKI: a three-dimensional Monte Carlo simulator for transfer of polarised light in planetary atmospheres

Abstract. Spectropolarimetry is a powerful tool for characterising planetary atmospheres and surfaces. For the design and operation of spectro(polari)metric instrumentation, numerically simulated signals of the measured radiation are essential. Here we present MONKI (Monte Carlo...

Dilaton physics from asymptotic freedom

The dilaton is investigated from first principles within an asymptotically free Gross-Neveu-Yukawa theory in three dimensions. In the limit of many fermion flavours, the theory features a finite line of strongly interacting fixed points. At its endpoint, a dilaton arises as the m...

Maximal elements in the Hurwitz graph

The Hurwitz graph has as its vertices the maximal chains in the lattice of non-crossing partitions, with an edge between two chains which differ at exactly one place. Adin and Roichman introduced an order on this graph by choosing a base element and showed that the maximal elemen...

An Efficient Mixed‐Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints

ABSTRACT This paper presents an efficient mixed‐integer nonlinear programming (MINLP) formulation for systems with discrete control inputs under minimum dwell time (MDT) constraints. By viewing such systems as switched systems, the problem is decomposed into a sequence optimizati...

Learning dissipative chaotic dynamics with boundedness guarantees

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven models that attempt to preserve invariant s...

Response Theory for Locally Gapped Systems

Abstract We introduce a notion of a local gap for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo’s formula for localized perturbations in such settings. On a high level, our result shows that the usual spectral gap condition, whic...

Stability of the expanding region of Kerr de Sitter spacetimes

We prove the nonlinear stability of the cosmological region of Kerr de Sitter spacetimes. More precisely, we show that solutions to the Einstein vacuum equations with positive cosmological constant arising from data on a cylinder that is uniformly close to the Kerr de Sitter geom...

On the attractor for 2D Navier–Stokes-like system with the dynamic slip boundary condition in a channel

Abstract We consider a 2D infinite channel domain with an incompressible fluid satisfying the so-called dynamic slip boundary condition on the (part of the) boundary. Introducing an exhaustion by a sequence of bounded sub-domains of the whole channel, we show that the unique weak...

Limits of Rauzy graphs of languages with subexponential complexity

To a subshift over a finite alphabet, one can naturally associate an infinite family of finite graphs, called its Rauzy graphs. We show that for a subshift of unbounded subexponential complexity, the Rauzy graphs converge in the sense of Benjamini–Schramm if and only if their emp...

A shrinking target problem in homogeneous spaces of semisimple algebraic groups

In this paper, we study a shrinking target problem with target at infinity in a homogeneous space of a semisimple algebraic group from the representation-theoretic point of view. Let 𝜌 : 𝐆 → 𝐆 𝐋 ⁡ ( 𝑉 ) be an irreducible ℚ -rational representation of a connected semisimple ℚ -alg...

Abundance theorem for minimal compact Kähler manifolds with vanishing second Chern class

In this paper, for compact Kähler manifolds with nef cotangent bundle, we study the abundance conjecture and the associated Iitaka fibrations. We show that, for a minimal compact Kähler manifold, the second Chern class vanishes if and only if the cotangent bundle is nef and the c...