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A key issue in tropical geometry is the lifting of intersection points to a non-Archimedean field. Here, we ask: Where can classical intersection points of planar curves tropicalize to? An answer should have two parts: first, identifying…
The three-dimensional generalized tropical climate model with partial viscosity and damping is considered in this paper. Global well-posedness of solutions of the three-dimensional generalized tropical climate model with partial viscosity…
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel…
Teleconnections between the tropical and the extratropical climates are often considered as a potential source of long-term predictability at seasonal to decadal time scales in the extratropics. This claim is taken up in the present work by…
This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed.…
One-dimensional (vertical) models of planetary atmospheres typically balance the net solar and internal energy fluxes against the net thermal radiative and convective heat fluxes to determine an equilibrium thermal structure. Thus,simple…
Abstractly, tropical hyperelliptic curves are metric graphs that admit a two-to-one harmonic morphism to a tree. They also appear as embedded tropical curves in the plane arising from triangulations of polygons with all interior lattice…
This paper presents numerical solutions and idealized analytical solutions of axisymmetric, $f$-plane models of the tropical cyclone boundary layer. In the numerical model, the boundary layer radial and tangential flow is forced by a…
In this study, we employ and modify the Lorenz energy cycle (LEC) framework as another way to understand the atmospheric circulation on tidally locked terrestrial planets. It well describes the atmospheric general circulation in the…
Cloud is critical for planetary climate and habitability, but it is also one of the most challenging parts of studying planets in and beyond the solar system. Here we use a cloud-resolving model (CRM) with high resolution (2 km) in a…
We consider the relevance of known constraints from each of Hide's theorem, the angular momentum conserving (AMC) model, and the equal-area model on the extent of cross-equatorial Hadley cells. These theories respectively posit that a…
A quasi-geostrophic intermediate complexity model is considered, providing a schematic representation of the baroclinic conversion processes which characterize the physics of the mid-latitudes atmospheric circulation. The model is relaxed…
A scalar field method to obtain transverse solutions of the vector Laplace and Helmholtz equations in spherical coordinates for boundary-value problems with azimuthal symmetry is described. Neither scalar nor vector potentials are used.…
Machine learning (ML)-based models have demonstrated high skill and computational efficiency, often outperforming conventional physics-based models in weather and subseasonal predictions. While prior studies have assessed their fidelity in…
The thermodynamics of electrowetting is treated. A general equation of electrowetting is derived from the first principles. It is demonstrated that the well-known Lippmann Equation describes a particular case of electrowetting when the…
We report first results on elliptic flow of identified particles at mid-rapidity in Au+Au collisions at $\sqrt{s_{_{NN}}}=130$ GeV using the STAR TPC at RHIC. The elliptic flow as a function of transverse momentum and centrality differs…
Using a hydrodynamic model, we predict the transverse momentum dependence of the spectra and the elliptic flow for different hadrons in Au+Au collisions at sqrt(s) = 130 A GeV. The dependence of the differential and p_t-integrated elliptic…
We use a 3D general circulation model to compare the primitive Martian hydrological cycle in "warm and wet" and "cold and icy" scenarios. In the warm and wet scenario, an anomalously high solar flux or intense greenhouse warming…
This paper describes the Habitable Energy balance model for eXoplaneT ObseRvations (HEXTOR), which is a model for calculating latitudinal temperature profiles on Earth and other rapidly rotating planets. HEXTOR includes a lookup table…
The notion of $p$-ellipticity has recently played a significant role in improving our understanding of issues of solvability of boundary value problems for scalar complex valued elliptic PDEs. In particular, the presence of $p$-ellipticity…