Related papers: Pattern orientation in finite domains without boun…
The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion…
The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type…
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…
We propose a method for unsupervised domain adaptation that trains a shared embedding to align the joint distributions of inputs (domain) and outputs (classes), making any classifier agnostic to the domain. Joint alignment ensures that not…
This paper investigates a diffusion process in a narrow tubular domain with reflecting boundary conditions, where the geometry serves as a singular perturbation of an underlying graph in $\mathbb{R}^2$ or $\mathbb{R}^3$. The construction…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
In the context of supervised statistical learning, it is typically assumed that the training set comes from the same distribution that draws the test samples. When this is not the case, the behavior of the learned model is unpredictable and…
Recent transport experiments in the original cuprate high temperature superconductor, {La$_{2-x}$Ba$_x$CuO$_4$}, have revealed a remarkable sequence of transitions and crossovers which give rise to a form of dynamical dimensional reduction,…
In this paper we introduce a new method to design control laws for non-linear underactuated systems. Our method produces an infinite dimensional family of control laws, whereas most control techniques only produce a finite dimensional…
The evolution of stripe patterns in type-I superconductors subject to a rotating in-plane magnetic field is investigated magneto-optically. The experimental results reveal a very rich and interesting behavior of the patterns. For small…
Stripe states in multilayer systems with perpendicular polarization are investigated by analytical calculations within a general continuum approach, applicable to ferromagnetic, ferroelectric, or ferroelastic nanoscale superlattices. The…
Non-topological defects such as grain boundaries abound in pattern forming systems, arising from local variations of pattern properties such as amplitude, wavelength, orientation, etc. We introduce the idea of treating such non-topological…
We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators for nonlinear systems with control inputs. To this end, we…
We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…
Domain adaptation deals with adapting classifiers trained on data from a source distribution, to work effectively on data from a target distribution. In this paper, we introduce the Nonlinear Embedding Transform (NET) for unsupervised…
We investigate the behavior of rotating incompressible flows near a non-flat horizontal bottom. In the flat case, the velocity profile is given explicitly by a simple linear ODE. When bottom variations are taken into account, it is governed…
We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…
Domain adaptation enables the learner to safely generalize into novel environments by mitigating domain shifts across distributions. Previous works may not effectively uncover the underlying reasons that would lead to the drastic model…