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11 views

Boundary Condition for LevelSet Reinitialization

Recently, I'm curious about the boundary condition of Levelset Reinitialization. Generally, when we try to express the interface, we use the levelset advection $$\phi_t + (V\cdot\nabla)\phi = 0$$ But ...
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62 views

How analyze the following fully nonlinear equation

Now I want to consider the following pde $u_t(x,t)=\sigma(x,t)(1+|D_xu(x)|^2)^{1/2}$, with initial condition $u(x,0)=g(x)$ which is analytic, and on domain $D\times \mathbf{R}^{+}$, $D\subset ...
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1answer
101 views

Network flows with shared capacities

Suppose we have a flow network, with capacity constraints on weighted sums of arc flows, such as: $$2 f(1, 2) + 3 f(4, 5) + f(3, 7) \leq 10,$$ where $f(1, 2)$ denotes the flow through arc $(1, ...
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83 views

Infinitesimal Generator of Billiard Flow

The Billiard flow $S_t$ on a Riemannian manifold with boundary (with corners) is the group of operators defined on continuous functions on the Co-sphere bundle as follows: To determine $S_t u(\xi)$, ...
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66 views

Parallelism degree of a DAG

Let me first give a motivation. Suppose a connected DAG G with one source X and one sink Y. The goal is to find some "bottleneck" node between X and Y, i.e. node through which every path from X to Y ...
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150 views

The geometric shape of domains of flows

Consider a smooth (non-compact) manifold $M$ with a vector field $X$. Then we know that there is a open neighbourhood $U \subseteq M \times \mathbb{R}$ of $M \times \{0\}$ such that on $U$ the flow ...
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1answer
348 views

Flow of an integer

I've stumbled across this family of flow networks, and posted the sequence of maximal flows to OEIS: A238729. I can't find any reference to it either. Has anyone seen it? Here is the description: ...
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1answer
205 views

Flows in word-hyperbolic groups

I was wondering if there is a good notion of flows in word-hyperbolic groups (maybe I should say flows in the Cayley graphs of word-hyperbolic groups). More precisely, I wonder if there is an ...
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247 views

Limits of $p/\ln p - q /\ln q$, $p, q$ prime

Is there any $\alpha>0$ for which there are known to exist two sequences of primes, $(p_i), (q_i)$ such that $$\alpha = \lim_{i\to\infty} \left(p_i/\ln p_i - q_i /\ln q_i\right)\ ?$$ The ...