Related papers: Singular paths spaces and applications
We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients. Asking only boundedness of the divergence of the coefficients (a classical condition in both the…
Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke…
In this article we consider the classical singular integral operator over a local field with rough kernels. We study the boundedness of such an operator on different function spaces by relaxing the smoothness condition on kernels.
Many seemingly disparate Markov chains are unified when viewed as random walks on the set of chambers of a hyperplane arrangement. These include the Tsetlin library of theoretical computer science and various shuffling schemes. If only…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…
Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem…
Let $X$ be a nonsingular projective surface over an algebraically closed field with characteristic zero, and $H_-$ and $H_+$ ample line bundles on $X$ separated by only one wall of type $(c_1,c_2)$. Suppose the moduli scheme $M(H_-)$ of…
We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or Stokes flow, are evaluated at points nearby. Such values could be needed in solving an integral…
We study transport within a spatially heterogeneous one-dimensional quantum walk with a combination of hierarchical and random barriers. Recent renormalization group calculations for a spatially disordered quantum walk with a regular…
Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…
It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution…
We develop a generalisation of the original theory of regularity structures, [Hai14], which is able to treat SPDEs on manifolds with values in vector bundles. Assume $M$ is a Riemannian manifold and $E\to M$ and $F^i\to M$ are vector…
We introduce an approach to study certain singular PDEs which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths. We illustrate its applicability on some model problems like…
The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often,…
Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scattering in the Born approximation is non-unitary, but both an example with…
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this…
Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
We make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\infty$ to $\infty$. The completeness…