Liouville
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Related Articles from SNS
Boundedness of Left Half-Plane Eigenvalues for Non-Selfadjoint Indefinite Sturm--Liouville Problems with Applications to Fourier Modal Methods
arXiv:2606.03537v1 Announce Type: cross Abstract: We study a general class of non-selfadjoint indefinite Sturm--Liouville problems of the form $$ -(p\,y')' q\,y = \lambda\, p\, y, $$ on a finite interval with complex-valued coefficients, where $p$ is piecewise in $W^{2,\infty}$, non-vanishing, and satisfies a non-degenerate interface condition, and $q$ is bounded. We prove that all eigenvalues in the open left half-plane are contained in a bounded set, which, by classical Sturm--Liouville...
Boundedness of Left Half-Plane Eigenvalues for Non-Selfadjoint Indefinite Sturm--Liouville Problems with Applications to Fourier Modal Methods
arXiv:2606.03537v1 Announce Type: new Abstract: We study a general class of non-selfadjoint indefinite Sturm--Liouville problems of the form $$ -(p\,y')' q\,y = \lambda\, p\, y, $$ on a finite interval with complex-valued coefficients, where $p$ is piecewise in $W^{2,\infty}$, non-vanishing, and satisfies a non-degenerate interface condition, and $q$ is bounded. We prove that all eigenvalues in the open left half-plane are contained in a bounded set, which, by classical Sturm--Liouville...
Two-dimensional fluorescence spectroscopy with quantum entangled photons: Idler-referenced timing without pump detection
Announce Type: replace Abstract: Entangled photons have attracted increasing interest as resources for developing time-resolved spectroscopic techniques. Theoretical studies suggest that their non-classical correlations enable time-resolved spectroscopy with monochromatic pumping and can selectively isolate specific Liouville pathways in nonlinear optical signals. In an earlier study, we proposed a fluorescence detection scheme that could, in principle, be implemented using existing...
Generalized flux-weighted boundary walls in kinetic models
Announce Type: replace-cross Abstract: We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary conditions parametrized by an integer $n$, corresponding to different velocity distributions imposed at the boundaries, generalizing the standard flux-weighted Maxwellian scheme. By combining Liouville's theorem with...
SPLIT-PINN: Separable Probability Learning Technique via Physics-Informed Neural Networks for High-Dimensional Probabilistic Modeling
arXiv:2606.04000v1 Announce Type: cross Abstract: We present a probabilistic modeling framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials. Spatially heterogeneous material state fields are represented using probability density functions (PDFs), providing a principled statistical description of microstructural variability and state evolution across different computational polycrystalline...
Logarithmic Sobolev inequality and hypercontractivity for the Navier-Stokes Fokker-Planck operator
Announce Type: cross Abstract: The stochastic incompressible Navier-Stokes equations on $\TT^3$, completed by the fluctuation-dissipation noise, have a Fokker-Planck generator that decomposes into a self-adjoint Ornstein-Uhlenbeck (dissipative) part and an antisymmetric (convective) part. We prove two results about this generator. First, the logarithmic Sobolev inequality holds with the same optimal constant as the pure Ornstein-Uhlenbeck operator, $c_\mathrm{LSI} = \nu\lambda_1$ (where...
Generalized flux-weighted boundary walls in kinetic models
arXiv:2604.24592v3 Announce Type: replace-cross Abstract: We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary conditions parametrized by an integer $n$, corresponding to different velocity distributions imposed at the boundaries, generalizing the standard flux-weighted Maxwellian scheme. By combining...