Related papers: Heat content determines planar triangles
Relativistic thermodynamics as result of some recent computer simulations is derived.
We present analytical and numerical results on the heat conduction in a linear mixing system. In particular we consider a quasi one dimensional channel with triangular scatterers with internal angles irrational multiples of pi and we show…
We use a probabilistic interpretation of solid angles to generalize the well-known fact that the inner angles of a triangle sum to 180 degrees. For the 3-dimensional case, we show that the sum of the solid inner vertex angles of a…
We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.
Using mesoscopic numerical simulations and analytical theory we investigate the coarsening of the solvent structure around a colloidal particle emerging after a temperature quench of the colloid surface. Qualitative differences in the…
The standard formula that describes the thermal expansion of a solid creates several puzzles for discerning students. Three puzzles are reviewed, and their common resolution discussed both conceptually and quantitatively.
In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of…
We study the heat content function, the heat trace function, and questions of isospectrality for the Laplacian with Dirichlet boundary conditions on a compact manifold with smooth boundary in the context of finite coverings and warped…
We study the dependence of the heat transfer between two semi-infinite solids on the dielectric properties of the bodies. We show that the heat transfer at short separation between the solids may increase by many order of magnitude when the…
This is a review of the observational and theoretical evidence for nanoflare heating of the magnetically-closed corona.
Let P be a set of n points in general position in the plane. We study the chromatic number of the intersection graph of the open triangles determined by P. It is known that this chromatic number is at least n^3/27+O(n^2), and if P is in…
Let $P$ be an operator of Dirac type and let $D=P^2$ be the associated operator of Laplace type. We impose spectral boundary conditions and study the leading heat content coefficients for $D$.
We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulation problem, which seeks to reconstruct…
We describe the statistics of checkerboard triangulations obtained by colouring black every other triangle in triangulations of convex polygons.
A sharp double-sided Harnack bound is derived for positive solutions of a fractional order heat equation.
In the first part, we introduce a notion a degree of edge-colorings of bicubic plane graphs and proves some local formula of the graded number of colorings. In the second part, we give a new proof of a result of Fisk saying that any two…
Let $\Omega$ be an open set in a complete, smooth, non-compact, $m$-dimensional Riemannian manifold $M$ without boundary, where $M$ satisfies a two-sided Li-Yau gaussian heat kernel bound. It is shown that if $\Omega$ has infinite measure,…
We prove that the homotopy type of a map from a Peano continuum into a planar or one-dimensional space is determined by the induced homomorphism of fundamental groups. This provides a new proof that planar sets are aspherical and is used to…
We prove Beurling's theorem for rank 1 Riemmanian symmetric spaces and relate it to the characterization of the heat kernel of the symmetric space.
We introduce the heat equation relative to a positive dd-bar-closed current and apply it to the invariant currents associated with Riemann surface laminations possibly with singularities. The main examples are holomorphic foliations by…