A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study finds multiple solutions for Van der Waals-Cahn-Hilliard equation on manifolds.
We give multiplicity results for the solutions of a nonlinear elliptic equation, with an asymmetric double well potential of Van der Waals-Allen--Cahn--Hilliard type, satisfying a linear volume constraint, on a bounded Lipschitz domain $Ω\subset\mathds R^N$. The number of solutions is estimated in terms of topological …
Proves generic nondegeneracy for solutions under volume constraint in closed manifolds.
We construct solutions of the Cahn-Hilliard equation whose nodal set converges to a given constant mean curvature hypersurface in a Riemannian manifold.
Proves existence of multiple solutions to a multiphasic equation on manifolds.
We prove that any limit-interface corresponding to a locally uniformly bounded, locally energy-bounded sequence of stable critical points of the van der Waals--Cahn--Hilliard energy functionals with perturbation parameter tending to 0 is supported by an embedded smooth stable minimal hypersurface in low dimensions and …
Multicomponent bilayer structures arise as the ubiquitous plasma membrane in cellular biology and as blends of amphiphilic copolymers used in electrolyte membranes, drug delivery, and emulsion stabilization within the context of synthetic chemistry. We develop the multicomponent functionalized Cahn-Hilliard (mFCH) free…
Improved prediction of polymer morphology through machine learning and simulations.
We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping properties of the corresponding biharmonic heat operator on certain Banach spaces. Thi…
Minimal submanifolds are found as energy concentration sets in variational problems.
FNOs learn solution operators of dissipative equations efficiently via spectral methods.
VANO uses neural operators for unsupervised learning of functional data.
Study of phase separation and geometry on a closed elastic curve, including dynamics and free energy minimization.
LiLaN uses linear latent networks to solve stiff ODEs efficiently.