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A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…
We perform a detailed study of an effective field theory which includes the Standard Model particle content extended by a pair of Weyl fermionic SU(2)-doublets with opposite hypercharges. A discrete symmetry guarantees that a linear…
We study when multiplication by a weight can turn a non-compact composition operator on H 2 into a compact operator, and when it can be in Schatten classes. The q-summing case in H p is considered. We also study when this multiplication can…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
Simplified models provide a useful way to study the impacts of a small number of new particles on experimental observables and the interplay of those observables, without the need to construct an underlying theory. In this study, we perform…
We discuss the phenomenology of a dark matter scenario in which we extend the Standard Model by a real scalar particle and a vector-like heavy quark. Such a model can be seen as a simplified version of a composite setup in which the scalar…
In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantum dynamics of electrons can be described by the…
The seesaw mechanism with three heavy Majorana right-handed neutrinos provides an elegant explanation for neutrino masses and, combined with leptogenesis, can generate the baryon asymmetry of the universe (BAU). Naturally embedded in a…
We study perturbations $(\tilde\tau_t)_{t\ge 0}$ of the semigroup of shifts $(\tau_t)_{t\ge 0}$ on $L^2(\R_+)$ with the property that $\tilde\tau_t - \tau_t$ belongs to a certain Schatten-von Neumann class $\gS_p$ with $p\ge 1$. We show…
We propose a novel mechanism in composite models that provides self-interacting dark matter along with the Higgs itself as composite particles, alleviating the Standard Model naturalness problem and explaining small-scale discrepancies such…
In this paper we use some ideas from \cite{FG-97, G-06} and consider the description of H\"{o}rmander type pseudo-differential operators on $\mathbb{R}^d$ ($d\geq1$), including the case of the magnetic pseudo-differential operators…
We present a high-order compact finite difference approach for a class of parabolic partial differential equations with time and space dependent coefficients as well as with mixed second-order derivative terms in $n$ spatial dimensions.…
It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of…
We consider perturbations of Minkowski space as well as more general spacetimes on which the wave operator $\square_g$ is known to be essentially self-adjoint. We define complex powers $(\square_g-i\varepsilon)^{-\alpha}$ by functional…
The purpose of this article is to study pseudospectral properties of the one-dimensional Schr\"{o}dinger operator perturbed by a complex steplike potential. By constructing the resolvent kernel, we show that the pseudospectrum of this…
This paper proposes a new method based on neural networks for computing the high-dimensional committor functions that satisfy Fokker-Planck equations. Instead of working with partial differential equations, the new method works with an…
We present the class of Hida-Mat\'ern kernels, which is the canonical family of covariance functions over the entire space of stationary Gauss-Markov Processes. It extends upon Mat\'ern kernels, by allowing for flexible construction of…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…